Publications

PUBLICATION LIST (google scholar link)

Chun Liu

Appeared:

1. (with Fang-Hua Lin) Nonparabolic Dissipative Systems Modeling the Flow of Liquid Crystals, Communications on Pure and Applied Mathematics, Vol. 48, Issue 5, 501 – 537 (1995). abstract

2. (with Fang-Hua Lin) Partial Regularity of the Dynamic System Modeling the Flow of Liquid Crystals, Discrete and Continuous Dynamic Systems, Vol 2, No 1, 1 – 23 (1996). abstract

3. (with David Kinderlehrer) Revisiting the Focal Conic Structures in Smectic A, Proceeding of Symposium on Elasticity to honor Professor J.L. Ericksen. ASME Mechanics and Materials Conference, 217 – 225 (1996). abstract

4. (with Sergio A. Alvarez) Motion of a Closed Curve by Minus the Surface Laplacian of Curvature, Differential and Integral Equations, Vol 13, No. 10-12, 1583–1594 (1997). abstract

5. (with David Kinderlehrer, Florin Manolache and Shlomo Ta’asan) Remarks about Analysis and Simulation of Grain Boundary Systems, Proceeding of Third International Conference of Grain Growth, 437 – 443 (1998).

6. (with M. Carme Calderer and Karl Voss) Radial Configurations of Smectic A materials and Focal Conics, Physica D, 124, 11—22 (1998). abstract

7. (with Noel J. Walkington) Approximation of Liquid Crystal Flows, Siam Journal of Numerical Analysis, Vol 37, 725–741 (2000). abstract

8. (with Fang-Hua Lin) Existence of Solutions for Ericksen-Leslie System, Archive for Rational Mechanics and Analysis, 154, no. 2, 135–156 (2000). abstract

9. (with M. Carme Calderer) Liquid Crystal Flow: Dynamic and Static Configurations, Siam Journal of Applied Mathematics 60 (6), 1925 – 1949 (2000). abstract

10. Dynamic Theory for Incompressible Smectic-A Liquid Crystals: Existence and Regularity, Discrete and Continuous Dynamic Systems, Vol 6, Num. 3, 591–608 (2000). abstract

11. (with M. Carme Calderer) Poiseuille Flow of Nematic Liquid Crystals, International Journal of Engineering Science, 38, 1007-1022 (2000). abstract

12. (with M. Carme Calderer) Mathematical Developments in the Study of Smectic A Liquid Crystals, International Journal of Engineering Science, 38, 1113-1128 (2000). abstract

13. (with David Kinderlehrer) Evolution of Grain Boundaries, Mathematical Models and Methods in Applied Sciences (M3AS), 11 (4) , 713–729 (2001). abstract

14. (with M. Carme Calderer and Karl Voss) Smectic A Liquid Crystal Configurations with Interface Defects, Mathematical Methods in the Applied Sciences, 24 (7), 473–489 (2001). abstract

15. (with Jie Shen) On Liquid Crystal Flows with Free-Slip Boundary Conditions, Discrete and Continuous Dynamic Systems, Vol 7, No. 2, 307–318 (2001). abstract

16. (with Noel J. Walkington) An Eulerian Description of Fluids Containing Visco-Elastic Particles, Archive for Rational Mechanics and Analysis, 159, 229–252 (2001). abstract

17. (with M. Carme Calderer, Dmitry Golovaty and Fanghua Lin) Time Evolution of Nematic Liquid Crystals with Variable Degree of Orientation, SIAM Journal on Mathematical Analysis, 33 (5), 1033–1047 (2001). abstract

18. (with Raimund Burger and Wolfgang Wendland) Existence and Stability for Mathematical Models of Sedimentation-Consolidation Processes in Several Space Dimensions, Journal of Mathematical Analysis and Applications, 264, 288–310 (2001). abstract

19. (with Fanghua Lin) Static and Dynamic Theories of Liquid Crystals, Journal of Partial Differential Equations, Vol 14, No. 4, 289–330 (2001). article

20. (with Qi Wang, Weinan E and Pingwen Zhang) Kinetic theory for flows of nonhomogeneous rodlike liquid crystalline polymers with a nonlocal intermolecular potential, Physical Review E, 65, 051504 (2002). abstract

21. (with Noel J. Walkington) Mixed Method for the Approximation of Liquid Crystal Flows, Mathematical Modelling and Numerical Analysis, Vol. 36, No. 2, pp. 205-222 (2002). abstract

22. (with M. Carme Calderer and Quan Shen) Axisymmetric Configurations of Bipolar Liquid Crystal Droplets, Continuum Mechanics and Thermodynamics, Vol 14, No. 4, 363–375 (2002). abstract

23. (with Bagisa Mukherjee) On Stability of Two Nematic Liquid Crystal Configurations, Discrete and Continuous Dynamic Systems B, Vol 2, No. 4, 561 –574 (2002). abstract

24. (with Patricia Bauman, M. Carme Calderer and Daniel Phillips) The Phase Transition Between Chiral Nematic and Smectic A* Liquid Crystals, Archive for Rational Mechanics and Analysis, 165, 2, 161 – 186 (2002). abstract

25. (with Jie Shen) A Phase Field Model for the Mixture of Two Incompressible Fluids and its Approximation by a Fourier-Spectral Method, Physica D, 179, 4, 211–228 (2003). abstract

26. (with Mingjun Lai and Paul Wenston) Bivariate Spline Method for Numerical Solution of Time Evolution Navier-Stokes Equations Over Polygons in Stream Function Formulation, Numerical Methods for Partial Differential Equations, Vol. 19, No. 6, 776–827 (2003). abstract

27. (with Mingjun Lai and Paul Wenston) Numerical Simulations on Two Nonlinear Biharmonic Evolution Equations, Applicable Analysis 83, no. 6, 563–577 (2004). abstract

28. (with Qiang Du and Xiaoqiang Wang) A Phase Field Approach in the Numerical Study of the Elastic Bending Energy for Vesicle Membranes, Journal of Computational Physics 198, no. 2, 450–468 (2004). abstract

29. (with Pengtao Yue, Jimmy Feng and Jie Shen) A Diffuse-Interface Method for Simulating Two-Phase Flows of Complex Fluids, Journal of Fluid Mechanics, Vol 515, 293–317 (2004). abstract

30. (with Fanghua Lin and Ping Zhang) On Hydrodynamics of Viscoelastic Fluids, Communication of Pure and Applied Mathematics, Vol 58, Issue 11, 1437 — 1471 (2005). abstract

31. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) A Phase Field Formulation of the Willmore Problem, Nonlinearity, 18, 1249 — 1267 (2005). abstract

32. (with Peng Yu and Qiang Du) From Micro to Macro Dynamics Via a New Closure Approximation to the FENE Model of Polymeric Fluids, SIAM Journal on Multiscale Modelling and Simulation, Vol 3, No 4, 895 — 917 (2005). abstract

33. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Modeling the spontaneous curvature effects in static cell membrane deformation by a phase field formulation, Communications in Pure and Applied Analysis, Vol 4, No 3, 537 — 548 (2005). abstract

34. (with Qiang Du and Xiaoqiang Wang) Retrieving Topological Information For Phase Field Models, SIAM Journal on Applied Mathematics, Vol 65, No 6, 1913 — 1932 (2005). abstract

35. (with Pengtao Yue, Jimmy Feng and Jie Shen) Interfacial Forces and Marangoni Flow on a Nematic Drop, Journal of Colloid and Interface Science, 290, 281 — 288 (2005). abstract

36. (with Qiang Du and Peng Yu) FENE dumbbell model and its several linear and nonlinear closure approximations, SIAM Journal on Multiscale Modeling and Simulation, Vol 4, No 3, 709 — 731 (2005). abstract

37. (with Pengtao Yue, Jimmy Feng and Jie Shen) Diffuse-Interface Simulations of Drop-Coalescence and Retraction in Viscoelastic Fluids, Journal of Non-Newtonian Fluid Dynamics, Vol 129, 163 — 176 (2005). abstract

38. (with Pengtao Yue, Jimmy Feng and Jie Shen) Viscoelastic Effects on Drop Deformation in Steady Shear, Journal of Fluid Mechanics, 540, 427 — 437(2005). abstract

39. (with Qiang Du and Xiaoqiang Wang) Simulating the Deformation of Vesicle Membranes under Elastic Bending Energy in Three Dimensions, Journal of Computational Physics, 212, 2, 757 — 777 (2006). abstract

40. (with Pengtao Yue, Jimmy Feng and Jie Shen) Transient drop deformation upon startup of shear in viscoelastic fluids, Physics of Fluids, 17, 123101 (2005). abstract

41. (with Rolf Ryham and Zhiqiang Wang) On Electro-Kinetic Fluids: One Dimensional Configurations, Discrete and Continuous Dynamical Systems B, Volume 6, Number 2, 357 — 371 (2006). abstract

42. (with Pengtao Yue, Jimmy Feng and Jie Shen) Variational Approach in Two-Phase Flows of Complex Fluids transport and induced elastic stress, in A. Miranville, editor, Mathematical Models and Methods in Phase Transitions,. Nova Publications, (2005). (21 pages)

43. (with Pengtao Yue, Jimmy Feng and Jie Shen) An Energetic Variational Formulation with Phase Field Methods for Interfacial Dynamics of Complex Fluids: Advantages and Challenges, in M.C. Calderer, E. Terentjev editors, ”Modeling of Soft Matter”, IMA Volumes in Mathematics and its Applications, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN (2005). (29 pages)

44. (with Fanghua Lin and Ping Zhang) On a Micro-Macro Model for Polymeric Fluids near Equilibrium, Communications on Pure and Applied Mathematics, Vol 60. Issue 6, 838—866 (2007). abstract

45. (with Ping Lin) Simulations of singularity dynamics in liquid crystal flows: a fast C0 Finite element approach, Journal of Computational Physics, 215 (1), 348–362 (2006). abstract

46. (with Carme Calderer and Baisheng Yan) A model for total energy of nematic elastomers with non-uniform prolate spheroids. Advances in applied and computational mathematics, Advances in applied and computational mathematics, 245–259, Nova Sci. Publ., Hauppauge, NY, (2006).

47. (with Xiaofeng Yang, Jimmy Feng and Jie Shen) Numerical Simulations of Jet Pinching-off and Drop Formation using an Energetic Variational Phase-Field Method, Journal of Computational Physics 218:417-428 (2006). abstract

48. (with C. Zhou, P. Yue, J Feng and Jie Shen) Heart-shaped bubbles rising in anisotropic liquids, Physics of Fluids, 19, 041703 (2007). abstract

49. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Diffusive Interface Energies Capturing the Euler Number: Relaxation and Renormalization, Communications of Mathematical Sciences 5, pp.233-242 (2007). article

50. (with Xiaobing Feng and Yinnian He) Analysis of finite element approximations of a phase field model for two phase fluids, Mathematics of Computation 76, no. 258, 539–571 (2007). abstract

51. (with Noel J. Walkington) Convergence of Numerical Approximations of the Incompressible Navier Stokes Equations with Variable Density and Viscosity, SIAM Journal of Numerical Analysis 45, no. 3, 1287–1304 (2007). abstract

52. (with Qiang Du and Manlin Li) Analysis of a Phase Field Navier-Stokes Vesicle-Fluid Interaction Model, Discrete and Continuous Dynamical Systems B, 8, No 3, pp.539-556, (2007). abstract

53. (with Zhen Lei and Yi Zhou) Global Existence for Small Strain Viscoelasticity, Communication in Mathematical Sciences 5, No 3, 595 — 616 (2007). article

54. (with Rolf Ryham and Ludmil Zikatanov) Mathematical Models for the Deformation of Electrolyte Droplets, Discrete and Continuous Dynamical Systems B, Volume 8, Number 3, 649 — 661 (2007). abstract

55. (with Ping Lin and Hui Zhang) An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics, Journal of Computational Physics, Volume 227, Issue 2, 1411 —1427 (2007). abstract

56. (with Zhen Lei and Yi Zhou) Global Solutions for Incompressible Viscoelastic Fluids, Archive for Rational Mechanics and Analysis 188, 371 – 398 (2008). abstract

57. (with Hailiang Liu) Boundary Conditions for the Microscopic FENE Models, SIAM Journal of Applied Mathematics Volume 68, Issue 5, 1304—1315 (2008). abstract

58. (with Yunkyong Hyon, Jose A. Carrillo and Qiang Du) A Macroscopic Closure Approximation to the Micro-Macro FENE Models with Maximum Entropy Principle for Polymeric Materials, Kinetic and Related Models, Volume 1, Number 2, 171 — 184 (2008). abstract

59. (with Ping Sheng and Jianwei Zhang) Onsager Principle and Electrorheological Fluid Dynamics, Progress of Theoretical Physics Supplement 175, 131 - 143 (2008). abstract

60. (with Aaron Naber and Jimmy Feng) The Nucleation and Growth of Gas Bubbles in a Newtonian Fluid: An Energetic Variational Phase Field Approach, in Moving Interface Problems and Applications in Fluid Dynamics (AMS Contemporary Mathematics Series, Vol. 466, eds. K. B. Cheong, Z. Li and P. Lin). pp. 95-120. American Mathematics Society (2008).

61. (with Yunkyong Hyon and Qiang Du) An Enhanced Macroscopic Closure Approximation to the Micro-macro FENE Models for Polymeric Materials, SIAM Journal of Multiscale Modeling and Simulation, Volume 7, Number 2, 978 — 1002 (2008). abstract

62. (with Jianwei Zhang, Xiuqing Gong, Weijia Wen and Ping Sheng) Electrorheological Fluid Dynamics, Physical Review Letters 101, 194503 (2008). abstract

63. (with Huan Sun) On Energetic Variational Approaches in Modeling the Nematic Liquid Crystal Flows, Discrete and Continuous Dynamical Systems, Volume 23, Number 2, 455 — 475 (2009). abstract

64. (with Qiang Du, Rolf Ryham and Xiaoqiang Wang) Energetic Variational Approaches to Modeling Vesicle and Fluid Interactions, Physica D, 238, 923—930 (2009). abstract

65. (with Pengtao Sun and Jinchao Xu) Phase Field Model of Thermo-Induced Marangoni Effects in the Mixtures and its Numerical Simulations with Mixed Finite Element Methods, Communications in Computational Physics, 6, 1095 — 1117(2009). abstract

66. (with Yunkyong Hyon and Do Young Kwak) Energetic Variational Approach in Complex Fluids : Maximum Dissipation Principle, Discrete and Continuous Dynamical Systems, Volume 26, Number 4, 1291 — 1304 (2010). abstract

67. (with Xiang Xu and Liyun Zhao) Axisymmetric Solutions to a coupled Navier-Stokes/Allen-Cahn Equations, SIAM Journal of Mathematical Analysis, Volume 41, Issue 6, 2246-2282 (2010). abstract

68. (with Qiang Du and Yunkyong Hyon) On some PDF based moment closure approximations of micro-macro models for viscoelastic polymeric fluids, Journal of Computational and Theoretical Nanoscience, 7, 738 — 755 (2010). abstract

69. (with Norifumi Sato and Yoshihiro Tonegawa) On the Existence of Mean Curvature Flow with Transport Term, Interfaces and Free Boundaries 12, No 2, 251-277 (2010). abstract

70. (with Huan Sun) The Slip Boundary Condition in the Dynamics of Solid Particles Immersed in Stokesian Flows, Solid State Communications, Volume 150, Issues 22, 990-1002 (2010). abstract

71. (with Yunkyong Hyon and Robert Eisenberg) Energy Variational Analysis EnVarA of Ions in Water and Channels: Field Theory for Primitive Models of Complex Ionic Fluids, Journal of Chemical Physics 133, 104104 (2010) . abstract

72. (with Shupeng Zhang and Hui Zhang) Numerical Simulations of Hydrodynamics of Nematic Liquid Crystals: Effects of Kinematic Transports, Communications in Computational Physics Vol. 9, No. 4, 974-993 (2010). abstract

73. (with Yunkyong Hyon and Robert Eisenberg) A Mathematical Model for the Hard Sphere Repulsion in Ionic Solutions, Communications in Mathematical Sciences 9(2), pp.459–475, 2011. article

74. (with Chiun-Chang Lee, Hijin Lee, Yunkyong Hyon and Taichia Lin) New Poisson-Boltzmann Type Equations: One-Dimensional Solutions, Nonlinearity 24, pp.431–458, 2011. abstract

75. (with Jinsong Hua, Ping Lin and Qi Wang) Energy Law Preserving C0 Finite Element Schemes for Phase Field Models in Two-Phase Flow Computations, Journal of Computational Physics 230, 7115 – 7131 (2011). abstract

76. (with James H. Adler, James Brannick, Thomas Manteuffel and Ludmil Zikatanov) First-order system least squares and the energetic variational approach for two-phase flow, Journal of Computational Physics 230(17):6647-6663 (2011). abstract

77. (with Xiaofeng Yang, M. Gregory Forest and Jie Shen) Shear Cell Rupture of Nematic Droplets in Viscous Fluids, Journal of Non-Newtonian Fluid Mechanics 166:487–499 (2011). abstract

78. (with Yoichiro Mori and Robert S. Eisenberg) A Model of Electrodiffusion and Osmotic Water Flow and its Energetic Structure, Physica D: Nonlinear Phenomena, 240(22), 1835-1852 (2011). abstract

79. (with Xiang Xu and Hao Wu) Asymptotic Behavior for a Nematic Liquid Crystal Model with Different Kinematic Transport Properties, Calculus of Variations and PDE’s, Volume 45, Issue 3-4, 319-345 (2012). abstract

80. (with Yunkyong Hyon, James E. Fonseca and Robert Eisenberg) Energy Variational Approach To Study Charge Inversion (Layering) Near Charged Wall, Discrete and Continuous Dynamical Systems - Series B, Volume 17, Issue 8, 2725-2743 (2012). abstract

81. (with Xinpeng Xu and Tiezheng Qian) Hydrodynamic Boundary Conditions for One-Component Liquid-Gas Flows on Non-isothermal Solid Substrates, Communications for Mathematical Sciences, Volume 10, Issue 4, 1027-1053 (2012). abstract

82. (with Norifumi Sato and Yoshihiro Tonegawa) Two-Phase Flow Problem Coupled with Mean Curvature Flow, Interfaces and Free Boundaries, Volume 14, Issue 2, 185–203 (2012). abstract

83. (with Tzyy-Leng Horng, Tai-Chia Lin and Robert Eisenberg) PNP equations with Steric Effects: a Model of Ion Flow through Channels, Journal of Physical Chemistry, 116 (37), 11422–11441 (2012). abstract

84. (with Xiang Xu and Hao Wu) On the General Ericksen-Leslie System: Parodi’s Relation, Well-posedness and Stability. Archive for Rational Mechanics and Analysis, Volume 208, Issue 1, 59-107, (2013). abstract

85. (with Xiaofeng Yang, M. Gregory Forest, Huiyuan Li, Jie Shen and Qi Wang) Numerical Investigation Of The Dynamics Of Drop Formation And Pitch-Off Using A Phase-Field Model For Two-Phase Complex Fluids, Journal of Computational Physics, Volume 236, 1, Pages 1-14 (2013). abstract

86. (with Pengtao Sun, Lixiang Zhang and Jinchao Xu) Full Eulerian modeling and effective numerical studies for the dynamic fluid-structure interaction problem, Contemporary Mathematics, Volume 586, 351-363, (2013). abstract

87. (with Yi Du and Qingtian Zhang) Blow-up criterion for compressible visco-elasticity equations in three dimensional space. Communication of Mathematical Sciences, Volume 12, Number 3, Pages: 473 –484 (2013). abstract

88. (with Shixin Xu and Ping Sheng) An Energetic Variational Approach for Ion Transport. Communications on Mathematical Sciences, Vol. 12, No. 4, pp. 779-789 (2014). abstract

89. (with Allen Flavell, Julienne Kabre, Michael Machen, Bob Eisenberg, and Xiaofan Li) A Conservative Finite Difference Scheme for Poisson-Nernst-Planck Equations. Journal of Computational Electronics, Vol. 13, 235-249 (2014). abstract

90. (with Li Wan, Shixin Xu, Maijia Liao, and Ping Sheng) Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model. Physical Review X, 4, 011042 (2014). abstract

91. (with Yunkyong Hyon and Robert Eisenberg) An Energetic Varitional Approach to Ion Channel Dynamics, Mathematical Methods in the Applied Sciences, Volume 37, Issue 7, Pages 952 (2014). abstract

92. (with Shixin Xu, Minxin Chen, Xingye Yue and Sheereen Majd) Modeling and Simulating Asymmetrical Conductance Changes in Gramicidin Pores. Molecular Based Mathematical Biology (MBMB), Volume 2, Issue 1, Page 34 (2014). abstract

93. (with Li Wan, Shixin Xu, Maijia Liao, and Ping Sheng) Self-Consistent Approach to Global Charge Neutrality in Electrokinetics: A Surface Potential Trap Model. Physics, Vol 34, Issue 9, Page 590 – 596 (2014). abstract

94. (with Minxin Chen and Xiantao Li) Computation of the Memory Functions in the Generalized Langevin Models for Collective Dynamics of Macromolecules, Journal of Computational Physics, 141, 064112 (2014). abstract.

95. (with Chia-Yu Hsieh, Yunkyong Hyon, Hijin Lee And Tai-Chia Lin) Transport Of Charged Particles: Entropy Production And Maximum Dissipation Principle, Journal of Mathematical Analysis and Applications, Vol 422, Page 309 – 336 (2015). abstract

96. (with Xiaofeng Yang and Jie Shen) Decoupled Energy Stable Schemes For A Phase-Field Model Of Two-Phase Incompressible Flows With Variable Density. Journal of Scientific Computing, Vol 62, Page 601-622 (2015). abstract

97. (with Hao Wu, Taichia Lin) Diffusion limit of kinetic equations for multiple species charged particles. Archive for Rational Mechanics and Analysis, Vol 215, 419-441 (2015). abstract

98. (with Wenrui Hao, Zhiliang Xu and Guang Lin) A Fictitious Domain Method with a Hybrid Cell Model for Simulating Motion of Cells in Fluid Flow, Journal of Computational Physics, Volume 280, Pages 345-362 (2015). abstract

99. (with Jerry Yang, Chao Mao and Xiantao Li) On the Cauchy-Born Approximation at Finite Temperature, Computational Materials Science, preprint, Volume 99, Pages 21 – 28 (2015). abstract

100. (with Geng Chen and Tao Huang) Finite time singularities for hyperbolic systems, SIAM Journal of Mathematical Analysis, 47(1), 758-785 (2015). abstract

101. (with Huan Sun, James Brannick and Tiezheng Qian) Diffuse Interface Method for Multiple Phase Materials: An Energetic Variational Approach, Journal of Numerical Mathematics, Vol. 8, No. 2, pp. 220–236 (2015). abstract

102. (with James Brannick and Arkadz Kirshtein) Dynamics of Multi-Component Flows: Diffusive Interface Methods With Energetic Variational Approaches, Reference Module in Materials Science and Materials Engineering (MATS), Elsevier (2015).

103. (with Jinchao Xu and Maximilian Metti) Energetically stable discretizations for charge transport and electrokinetic models, Journal of Computational Physics, Volume 306, 1–18 (2016). abstract

104. (with Maijia Liao, Li Wan, Shixin Xu, and Ping Sheng) The Poisson Boltzmann equation and the charge separation phenomenon at the silica-water interface: A holistic approach, Annals of Mathematical Sciences and Applications Volume 1, Number 1, 217 - 49 (2016). abstract

105. (with Chiun-Chang Lee, Hijin Lee, YunKyong Hyon and Tai-Chia Lin) Boundary layer solutions of Charge Conserving Poisson-Boltzmann equations: one-dimensional case, Communications in Mathematical Sciences, Vol 14, Number 4, 911-940 (2016). abstract

106. (with Tao Huang, Fanghua Lin and Changyou Wang) Finite time singularity of the nematic liquid crystal flow in dimension three Archive for Rational Mechanics and Analysis, Vol 221, Issue 3, 1223-1254 (2016). abstract

107. (with Yong Wang and Zhong Tan) A Generalized Poisson-Nernst-Planck-Navier-Stokes Model on the Fluid with the Crowded Charged Particles: Derivation and its Well-Posedness, SIAM Journal of Mathematical Analysis, Vol. 48, No. 5, pp. 3191 - 3235 (2016). abstract

108. (with Lina Ma and Xiantao Li) From Generalized Langevin Equations to Brownian Dynamics and Embedded Brownian Dynamics, Journal of Chemical Physics, 145, 114102 (2016). abstract

109. (with Barbora Benešová, Johannes Forster, Carlos Garcia-Cervera and Anja Schlomerkemper) Analysis of the Flow of Magnetoelastic Materials, Proceedings in Applied Mathematics and Mechanics, 14 September 2016. abstract

110. (with Masakazu Endo, Yoshikazu Giga and Dario Gotz) Stability of a two-dimensional Poiseuille-type flow for a viscoelastic fluid, Journal of Mathematical Fluid Mechanics, 19 (1) 17 - 45 (2017). abstract

111. (with Yong Wang and Zhong Tan) Well-posedness on a new hydrodynamic model of the fluid with the dilute charged particles , Journal of Differential Equations, 262 (1), 68 - 115 (2017). abstract

112. (with Lina Ma and Xiaotao Li) Fluctuation-dissipation theorem consistent approximation of the Langevin dynamics model, Communication of Mathematical Sciences, Vol. 15, No. 4, 1171-1181 (2017). abstract

113. (with Cao Deng) Largest well-posed spaces for the general diffusion system with nonlocal interactions, Journal of Functional Analysis, Vol 272, Issue 10, 4030 - 4062 (2017). abstract

114. (with Lina Ma and Xiantao Li) The derivation and approximation of coarse-grained dynamics from the Langevin dynamics The Journal of Chemical Physics, 145, 204117 (2017). abstract

115. (with Pei Liu and Zhenli Xu) Generalized Schockley-Ramo Theorem in Electrolytes, Communications in Mathematical Sciences 15 , no. 2, 555–564. (2017). abstract

116. (with Hajime Koba and Yoshikazu Giga) Energetic variational approaches for incompressible fluid systems on an evolving surface, Quarterly of Applied Mathematics 75 , no. 2, 359–389. (2017) . abstract

117. (with Qiuju Xu, Andrew Belmonte, Russ Deforest and Zhong Tan) Strong Solutions and Instability to the Fitness Gradient System, Journal of Differential Equations 262, no. 7, 4021–4051 (2017). abstract

118. (with Jie Jiang and Yinghua Li) Two-Phase Incompressible Flows with Variable Density: An Energetic Variational Approach, Discrete and Continuous Dynamic Systems, Series A, 37 no. 6, 3243–3284. (2017). abstract

119. (with Daoyuan Fang and Chenyin Qian) On Partial Regularity Problem for 3D Boussinesq Equations, Journal of Differential Equations, Vol 263, Issue 7, 4156 - 4221 (2017). abstract

120. (with Arkadz Kirshtein and Mi-Ho Giga) Variational Modeling And Complex Fluids, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids edited by Anton Novotny and Yoshikazu Giga (2018). abstract

121. (with Fanghua Lin and Xianpeng Hu) Equations for Viscoelastic Fluids, Handbook of Mathematical Analysis in Mechanics of Viscous Fluids edited by Anton Novotny and Yoshikazu Giga (2018). abstract

122. (with Barbora Benešová, Johannes Forster, and Anja Schlömerkemper) Existence of weak solutions to an evolutionary model for magnetoelasticity, SIAM Journal of Mathematical Analysis, 50(1), 1200–1236 (2018). abstract

123. (with Francesco De Anna) Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamics-consistency Archive of Rational Mechanics and Analysis Volume 231, Issue 2, pp 637–717 (2018). abstract

124. (with Nir Gavish and Bob Eisenberg) Do Bi-Stable Steric Poisson-Nernst-Planck Models Describe Single Channel Gating? Journal of Physical Chemistry B, , 122 (20), pp 5183–5192 (2018). abstract

125. (with Qingcheng Yang, Arkadz Kirshtein, Yanzhou,  Jie Shen and Long-Qing Chen) A Thermodynamically Consistent Phase-Field Model for Viscous Sintering, Journal of the American Ceramic Society, 00:1–12 (2018). abstract

126. (with Anna Terebus and Jie Liang) Discrete Flux and Velocity Fields of Probability and Their Global Maps in Reaction Systems, Journal of Chemical Physics, 149, 185101 (2018). abstract

127. (with Pei Liu and Simo Wu) Non-Isothermal Electrokinetics: Energetic Variational Approach Communication in Mathematical Sciences, Vol. 16, No. 5, 1451-1463 (2018). abstract

128. (with Tatsu-Hiko Miura and Yoshikazu Giga) An energetic variational approach for nonlinear diffusion equations in moving thin domains, Advances in Mathematical Sciences and Applications, Vol 27, No. 1, pp.115 - 141 (2018). abstract

129. (with Tzyy-Leng Horng, Francisco Bezanilla and Bob Eisenberg) Continuum Gating Current Models Computed with Consistent Interactions Biophysical Journal, Volume 116, Issue 2, Pages 270-282 (2019). abstract

130. (with Xiantao Li and Lina Ma) Coarse-graining Langevin dynamics using reduced-order techniques Journal Of Computational Physics, Volume 380, Pages 170-190 (2019). abstract

131. (with Chenghua Duan, Cheng Wang and Xingye Yue) Numerical Methods for Porous Medium Equation by an Energetic Variational Approach, Journal Of Computational Physics 385, 13 – 32 (2019). abstract

132. (with Hao Wu) An Energetic Variational Approach for the Cahn-Hilliard Equation with Dynamic Boundary Conditions: Derivation and Analysis Archive of Rational Mechanics and Analysis, Volume 233, Issue 1, page 167?247 (2019). abstract

133. (with Chenghua Duan, Cheng Wang and Xingye Yue) Numerical Completer Solution for Random Genetic Drift by Energetic Variational Approach, ESAIM: Mathematical Modelling and Numerical Analysis, 53, 615–634 (2019). abstract

134. (with Xinfu Chen, Shixin Xu and Xingye Yue) Numerical Method for Multi-Alleles Genetic Drift Problem, SIAM Journal of Numerical Analysis Vol. 57, No. 4, pp. 1770–1788 (2019). abstract

135. (with Minxin Chen, Shixin Xu, Xingye Yue and Ran Zhang) Behavior of different numerical schemes for random genetic drift, BIT Numerical Mathematics Volume 59, Issue 3, pp 797?821— (2019). abstract

136. (with Anna Terebus and Jie Liang.) Discrete and Continuous Models of Probability Flux of Switching Dynamics: Uncovering Stochastic Oscillations in Toggle-Switch System The Journal of Chemical Physics, 151, 185104 (2019). abstract

137. (with Min-Jhe Lu and Shuwang Li) Nonlinear simulation of anelastic tumor-host interface, Volume 7, Issue 1, 25 - 47, Computational and Mathematical Biophysics (2019). abstract

138. (with Chenghua Duan, Cheng Wang and Xingye Yue) Convergence analysis of a numerical scheme for the porous medium equation by an energetic variational approach Numerical Mathematics: Theory, Methods and Application, Vol 13, No 1, pp. 63 - 80 (2020) abstract

139. (with Chia-Yu Hsieh, Tai-Chia Lin and Pei Liu) Global Existence of the Non-isothermal Poisson–Nernst–Planck–Fourier System Journal of Differential Equations, Volume 269, Issue 9, Pages 7287-7310 (2020). abstract

140. (with Arkadz Kirshtein and James Brannick) Analysis of the energy dissipation laws in thermodynamically consistent multi-component phase field models, Communication in Mathematical Sciences, Volume 18, Issue 3, pp. 875-885 (2020). abstract

141. (with Min-Jhe Lu, John Lowengrub and Shuwang Li) Complex far-field geometries determine the stability of solid tumor growth with chemotaxis, 83, 39, Bulletin of Mathematical Biology (2020) abstract

142. (with Yiwei Wang) On Lagrangian schemes for the multidimensional porous medium equations: a discrete energetic variational approach. Journal of Computational Physics Volume 417, 15 September 2020, 109566 (2020). abstract

143. (with Qing Cheng and Jie Shen) A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates. Journal of Computational Physics Volume 419, 15 October 2020, 109509 (2020). abstract

144. (with Qing Cheng and Jie Shen) A New Lagrange Multiplier Approach For Gradient Flows. Computer Methods in Applied Mechanics and Engineering, Vol 367, 113070 (2020). abstract

145. (with Ying Yang, Ming Tang, Benzhuo Lu and Liu-Qiang Zhong) Superconvergent Gradient Recovery for Nonlinear Poisson-Nernst-Planck equations with Applications to the Ion Channel Problem. Advance in Computational Mathematics 46, 78 (2020). abstract

146. (with Yiwei Wang, Pei Liu, and Bob Eisenberg) Field Theory of Reaction-Diffusion: Mass Action with an Energetic Variational Approach Physical Review E, 102, 062147 (2020). abstract

147. (with Yiwei Wang) A Variational Lagrangian Scheme for a Phase Field Model: A Discrete Energetic Variational Approach. SIAM Journal on Scientific Computing, 42(6), B1541–B1569 (2020). abstract

148. (with Chenghua Duan, Wenbin Chen, Xingye Yue, and Shenggao Zhou) Structure-Preserving Numerical Methods for Nonlinear Fokker–Planck Equations with Nonlocal Interactions by an Energetic Variational Approach. SIAM Journal on Scientific Computing, 43(1), B82–B107. (2020) abstract

149. (with Simo Wu and Ludmil Zikatanov) Energetic Stable Discretization for Non-Isothermal Electrokinetics Model, Journal of Computational Physics, Volume 425, 109889 (2021). abstract

150. (with Patrik Knopf, Kei Fong Lam and Stefan Metzger) Phase-field dynamics with transfer of materials: The Cahn–Hillard equation with reaction rate dependent dynamic boundary conditions. ESAIM: Mathematical Modelling and Numerical Analysis 55, 229–282 (2021). abstract

151. (with Qing Cheng and Jie Shen) Generalized SAV approaches for gradient systems, Journal of Computational and Applied Mathematics, Available online 10 March 2021, 113532. abstract

152. (with Yiwei Wang and Teng-Fei Zhang) A two species micro-macro model of wormlike micellar solutions and its maximum entropy closure approximations: An energetic variational approach. Journal of Non-Newtonian Fluid Mechanics, Volume 293, 104559 (2021). abstract

153. (with Yiwei Wang, Jiuhai Chen and Lulu Kang) Particle-Based Energetic Variational Inference, Statistics and Computing, 31, 34 (2021). abstract

154. (with Yekaterina Epshteyn and Masashi Mizuno) Motion of grain boundaries with dynamic lattice misorientations and with triple junctions drag. SIAM Journal of Mathematical Analysis, Vol. 53, No. 3, 3072-3097 (2021). abstract

155. (with Cheng Wang and Yiwei Wang) A Structure-preserving, Operator Splitting Scheme for Reaction-Diffusion Equations involving Law of Mass Action. Journal of Computational Physics, Volume 436, 110253 (2021). abstract

156. (with Cheng Wang, Steven Wise, Xingye Yue and Shenggao Zhou) A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system. Mathematics of Computation, 90 (331), 2021, 2071-2106 (2021). abstract

157. (with Yekaterina Epshteyn and Masashi Mizuno) Large time asymptotic behavior of grain boundaries motion with dynamic lattice misorientations and with triple junctions drag. Communication of Mathematical Sciences, 19, 5, 1403 – 1428 (2021). abstract

158. (with Patrik Knopf) On second-order and fourth-order elliptic systems consisting of bulk and surface PDEs: Well-posedness, regularity theory and eigenvalue problems. Interfaces and Free Boundaries (IFB) of European Mathematical Society, 23, 4, 507 – 533 (2021). abstract

159. (with Steve Wise, Cheng Wang and Yiwei Wang) Convergence Analysis Of The Variational Operator Splitting Scheme For A Reaction-Diffusion System With Detailed Balance, SIAM Journal of Numerical Analysis Vol. 60, Iss. 2 (2022). abstract

160. (with Jan-Eric Sulzbach) The Brinkman-Fourier System with Ideal Gas Equilibrium, to appear in Discrete and Continuous Dynamic Systems, 42(1): 425-462. (2022). abstract

161. (with.Cheng Wang, Steven M. Wise, Xingye Yue and Shenggao Zhou) An iteration solver for the Poisson-Nernst-Planck system and its convergence analysis, Journal of Computational and Applied Mathematics 406, 114017 (2022) abstract

162. (with Qing Cheng, Pourya Delafrouz, Jie Liang and Jie Shen) Modeling And Simulation Of Cell Nuclear Architecture Reorganization Process, Journal of Computational Physics, 449, 110808 (2022). abstract

163. (with Chenghua Duan, Wenbin Chen, Cheng Wang, and Xingye Yue) A second order, energy stable numerical scheme for the porous medium equation by an energetic variational approach. Communication of Mathematical Sciences, Volume 20, Number 4, 978 – 1024 (2022). abstract

164. (with Yiwei Wang and Teng-Fei Zhang) Dynamical Stability on a Micro-Macro Model for a Reactive Polymeric Fluid, Calculus of Variations and Partial Differential Equations 61(3), 1-37. (2022). abstract

165. (with Yiwei Wang) Some Recent Advances in Energetic Variational Approaches Entropy 24(5), 721 (2022). abstract

166. (with Chenghua Duan, Wenbin Chen, Cheng Wang and Shenggao Zhou) Convergence analysis of structure-preserving numerical methods for nonlinear Fokker-Planck equations with nonlocal interactions, Mathematical Methods in the Applied Sciences Volume45, Issue7 Pages 3764-3781, 2022. abstract

167. (with Jiangyan Liang, Ning Jiang, Yiwei Wang and Teng-Fei Zhang) On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit, Journal of Differential Equations Volume 309, Pages 427-454. 2022. abstract

168. (with Yiwei Wang and Bob Eisenberg) On variational principles for polarization responses in electromechanical systems, Communication in Mathematical Sciences Vol. 20, No. 6, pp. 1541–1550 (2022). abstract

169. (with Zhenlin Guo, Ping Lin, and John Lowengrub,) Second order approximation for a quasi-incompressiable Navier-Stokes Cahn-Hilliard system of two-phase flows with variable density, Journal Of Computational Physics, Volume 448, 1 January 2022, 110727. abstract

170. (with Ning-An Lai and Andrei Tarfulea) Positivity of temperature for some non-isothermal fluid models, Journal of Differential Equations, Volume 339, 5 December 2022, Pages 555-578 (2022). abstract

171. (with Katayun Barmak, Anastasia Dunca, Yekaterina Epshteyn and Masashi Mizuno) Grain Growth and the Effect of Different Time Scales, Association for Women in Mathematics Series ”Research in the Mathematics of Materials Science” , Editors Malena I. Español, Marta Lewicka, Lucia Scardia and Anja Schlömerkemper, Springer, Page 33 – 58 (2022).

172. (with Xiang Ji, Pei Liu, and Shenggao Zhou) Energetic Variational Approach for Prediction of Thermal Electrokinetics in Charging and Discharging Processes of Electrical Double Layer Capacitors, Journal of Power Sources, Volume 551, 232184 (2022). abstract

173. (with Yekaterina Epshteyn, Chang Liu and Masashi Mizuno) Nonlinear inhomogeneous Fokker-Planck models: energetic-variational structures and long time behavior, to appear in Analysis and Applications (AA) Vol. 20, No. 06, pp. 1295-1356 (2022). abstract

174. (with Jan-Eric Sulzbach) Well-Posedness for the Reaction-Diffusion Equation with Temperature in a Critical Besov Space, Journal of Differential Equations Volume 325, 15, Pages 119-149 (2022). abstract

175. (with Min-Jhe Lu, Wenrui Hao, Shuwang Li and John Lowengrub) Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis, Journal of Computational Physics Volume 459, 111153 (2022). abstract

176. (with Yuzhe Qin, Huaxiong Huang, Yi Zhu and Shixin Xu) A phase field model for mass transport with semi-permeable interfaces, Journal of Computational Physics Volume 464, 111334 (2022). abstract

177. (with Yekaterina Epshteyn and Masashi Mizuno) A Stochastic model of grain boundary dynamics: A Fokker-Planck perspective, Mathematical Models and Methods in Applied Sciences (M3AS) Vol. 32, No. 11, pp. 2189-2236 (2022). abstract

178. (with Yiwei Wang and Cheng Wang) A second-order accurate, operator splitting scheme for reaction-diffusion systems in an energetic variational formulation, SIAM Journal on Scientific Computing Vol. 44, Issue. 4 (2022). abstract

179. (with J. M. Rickman, K. Barmak and Y. Epshteyn) Point Process Microstructural Model of Metallic Thin Films with Implications for Coarsening npj Computational Materials 9, Article number: 27 (2023). abstract

180. (with Yekaterina Epshteyn, Chang Liu and Masashi Mizuno) Local well-posedness of a nonlinear Fokker-Planck model, Nonlinearity Volume 36, Number 3, 1890-1927 (2023). abstract

181. (with Qingcheng Yang, Yongxin Gao, Arkadz Kirshtein and Qiang Zhen) An Interfacially Consistent Phase-Field Model for Solid-State Sintering without Artificial Void Generation, Computational Materials Science, Volume 229, 5 October 2023, 112387 (2023). abstract

182. (with Cheng Wang, Steven Wise, Xingye Yue and Shenggao Zhou) A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis, Journal of Scientific Computing, 97, 23 (2023). abstract

183. (with Guosheng Fu) High-order variational Lagrangian schemes for compressible fluids, Journal of Computational Physics, Volume 491 , 15 October 2023, 112398 abstract

184. (with Chi-An Chen, Xiaofan Li and Yubin Lu) Finite Difference Approximation with ADI Scheme for Two-dimensional Keller-Segel Equations. Communications in Computational Physics 35, pp. 1352-1386 (2024). abstract

185. (with Ziqing Hu, Yiwei Wang and Zhiliang Xu) Energetic Variational Neural Network Discretizations to Gradient Flows, SIAM Journal on Scientific Computing, Vol. 46, Iss. 4 (2024). abstract

186. (with Francesco De Anna, Anja Schlömerkemper and Jan-Eric Sulzbach) Temperature dependent extensions of the Cahn-Hilliard equation, Nonlinear Analysis: Real World Applications, Volume 77, June 2024, 104056. abstract

187. (with Lulu Kang, Yuanxing Cheng and Yiwei Wang) Energetic Variational Gaussian Process Regression. WSC ’24: Proceedings of the Winter Simulation Conference Pages 3542 - 3553 (2024) abstract

188. (with Xuelian Bao and Yiwei Wang) A deterministic particle based scheme to micro-macro models of dilute polymeric fluids, Journal of Computational Physics Volume 522, 1 February 2025, 113589. abstract

189. (with Jan-Eric Sulzbach and Yiwei Wang) On a Continuum Model for Random Genetic Drift: A Dynamical Boundary Condition Approach. Communications in Analysis and Mechanics, Volume 17, Issue 3: 829-848 (2025). abstract

190. (with Wenrui Hao, Yiwei Wang and Yahong Yang) On pattern formation in the thermodynamically-consistent variational Gray-Scott model. Mathematical Biosciences, Volume 385, July 2025, 109453 (2025). abstract

191. (with Kobra Rabiei, Jeffrey R. Petrella, Suzanne Lenhart, and Wenrui Hao for the Alzheimer's Disease Neuroimaging Initiative)  Data-Driven Modeling of Amyloid-beta Targeted Antibodies for Alzheimer’s Disease. npj Systems Biology and Applications volume 11, Article number: 134 (2025). abstract

192. (with.Jan-Eric Sulzbach and Yiwei Wang) Non-isothermal diffuse interface model for phase transition and interface evolution, SIAM Journal on Applied Mathematics Vol. 85, Iss. 6, 10.1137/24M1685572 (2025). abstract

193. (with Cheng Wang and Yiwei Wang) On a positive-preserving, energy-stable numerical scheme to mass-action kinetics with detailed balance. Communication in Mathematical Sciences, Volume 23, Number 5, pp. 1447-1458 (2025). abstract

194. (with Yingdong Chen, Lulu Kang and Yiwei Wang) A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel, Journal of Statistical Theory and Practice, Volume 20, article number 100 (2026). abstract

Accepted:

1. (with Xiaofan Li, Qi Tang and Yiwei Wang ) Structure-Aware Variational Learning of a Class of Generalized Diffusions. to appear in Physica D: Nonlinear Phenomena (2026). abstract

2. (with Yiwei Wang) Thermodynamically Consistent Modeling of ATP-Driven Cross-Bridge Dynamics in Muscle Contraction. to appear in Biophysical Journal (2026). abstract

3. (with Baoli Hao, Ulisses Braga-Neto, Lifan Wang and Ming Zhong) Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter. to appear in Foundations of Data Science (2026). abstract

4. (with Qingqing Zhang, Chenghua Duan, Cheng Wang and Xingye Yue) A structure-preserving numerical method for a radially symmetric solution of porous medium equation, to appear in Journal of Scientific Computing (2026). abstract

5. (with Chenghua Duan and Xingye Yue) The Cumulative Distribution Function Based Method for Random Drift Model. to appear in Journal of Computational Mathematics (2026). abstract

6. (with Yubin Lu, Xiaofan Li, Qi Tang and Yiwei Wang) Learning Generalized Diffusions using an Energetic Variational Approach. to appear in Communications in Computational Physics (2025). abstract

Other Publications:

1. The Stability of the Radial Solution of the Ginzburg-Landau Equation with Magnetic Fields, (1997).

2. Variational Approaches in Complex Fluids, Lecture Notes (2004).

3. (with Hiroki Fukagawa and Takeshi Tsuji) A variational formulation for dissipative fluids in inhomogeneous temperature, Research Notes (2014).

4. Multi-scale Phenomena in Complex Fluids: Modeling, Analysis and Numerical Simulations (Series in Contemporary Applied Mathematics) (Series in Contemporary Applied Mathematics Cam) by Thomas Y. Hou (Author, Editor), Chun Liu (Editor), Jian-guo Liu (Editor), World Scientific Publishing Company ( 2009). abstract and contents

5. Nonlinear Conservation Laws, Fluid Systems and Related Topics (Series in Contemporary Applied Mathematics) by Gui-Qiang Chen (Author, Editor), Ta-Tsien Li (Editor), Chun Liu (Editor), World Scientific Publishing Company ( 2009). abstract and contents

6. Energetic Variational Approaches for Complex Fluids. Proceeding of the 36th Sapporo Symposium on Partial Differential Equations, August 22 - 24, 2011, Faculty of Science, Hokkaido University (2011). abstract