Listed by research areas
Published or accepted:
Active scalar equations:
(with Susan Friedlander) On a class of forced active scalar equations with small diffusive parameters, Pure and Applied Functional Analysis 8(1) (2023), 215–241. Preprint available on arXiv:2011.08454.
(with Susan Friedlander) Correction to: Wellposedness and Convergence of Solutions to a Class of Forced Non-diffusive Equations with Applications, J. Math. Fluid Mech. 23 (2021), 81.
(with Susan Friedlander) Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations, Arch. Rational Mechanics Ana. 240 (2021), no. 3, 1431–1485. Preprint available on arXiv:2005.10667.
(with Susan Friedlander) Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications, J. Math. Fluid Mech. 21 (2019), 21–50. Preprint available on arXiv:1902.04366.
(With Susan Friedlander) Solutions to a class of forced drift-diffusion equations with applications to the magneto-geostrophic equations, Annals of PDE (2018), 4(2):14. Preprint available on arXiv:1705.06417.
(with Susan Friedlander) Existence, uniqueness and regularity results for the viscous magneto-geostrophic equation, Nonlinearity, Vol. 28 (2015), no. 9, pp. 3193–3217. Preprint available on arXiv:1411.1980.
Chemotaxis system:
(with Tong Li) Existence of intermediate weak solution to the equations of three-dimensional chemotaxis systems, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 36 (2016), no. 2, pp. 861–875.
(with Tong Li, Michael Winkler and Chuan Xue) Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms, Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 25 (2015), no. 04, pp. 721–746.
Harmonic analysis:
(With Qasim Khan, Hassan Khan and Poom Kumam) Comparative analysis of fractional dynamical systems with various operators, AIMS Mathematics (2023), 8(6), pp. 13943–13983.
(With K.L. Cheung, K.P. Ho and T.L. Yee) Spherical Maximal Function on Local Morrey Spaces with Variable Exponents, Vietnam J. Math., Volume X (2022), Number X, XXXX–XXXX.
(With K.L. Cheung, K.P. Ho and T.L. Yee) Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents, Mathematical Inequalities & Applications, Volume 23 (2020), Number 4, 1509–1528.
Kinematic dynamo equations:
(with Susan Friedlander) Holder continuity of solutions to the kinematic dynamo equations, J. Math. Fluid Mech. 16 (2014), 691-700. Preprint available on arXiv:1404.0691.
Magnetohydrodynamics equations:
Global regularity for the 3D compressible magnetohydrodynamics with general pressure, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 42 (2022), no. 6, pp. 2927-2943. Preprint available on arXiv:2012.02971.
Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations, J. Diff. Eqns, Vol. 268 (6) (2020), 2622-2671.
Corrigendum: A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 35 (2015), no. 3, 1387-1390.
A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 33 (2013), no. 8, 3791-3805.
(with David Hoff) Global low-energy weak solutions of the equations of 3D compressible magnetohydrodynamics, Arch. Rational Mechanics Ana. 205 (2012), no. 1, 27-58.
Navier Stokes equations:
Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure, Z. Angew. Math. Phys. (ZAMP) 73, 18 (2022).
Some Serrin type blow-up criteria for the three-dimensional viscous compressible flows with large external potential force, Math. Methods Appl. Sci, Vol. 45 (2022), no. 4, 2072-2086.
Existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force, J. Diff. Eqns, Vol. 299 (2021), 463-521.
(With K.L. Cheung) Existence and Uniqueness of Small Energy Weak Solution to multi- dimensional compressible Navier-Stokes Equations with Large External Potential Force, Journal of Mathematical Physics, Vol. 57 (2016), no. 8, 081513, pp. 1–19.
Existence of global weak solution to Navier-Stokes equations with large external potential force and general pressure, Math. Methods Appl. Sci., Vol. 37 (2014), no. 17, 2716-2727.
Global Solutions of the Navier-Stokes Equations for Isentropic Flow with Large External Potential Force, Z. Angew. Math. Phys. (ZAMP), Vol. 64 (2013), no. 3, 767-784.
Navier-Stokes-Poisson system:
Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 40 (2020), no. 3, 1775-1798.
Viscoelastic flow:
Nonexistence of self-similar singularities in the ideal viscoelastic flow, Electron. J. Diff. Equ., Vol. 2012 (2012), no. 93, 1-7.
Thesis:
Global low-energy weak solutions of the equations of 3D magnetohydrodynamics, Thesis (Ph.D.), Indiana University, 2012.
Survey on Heegaard Floer Homology, Thesis (M.Phil.), Chinese University of Hong Kong, 2007.
Preprints:
Uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. Preprint available on arXiv:2012.07028.
Large friction limit of the compressible Navier-Stokes equations with Navier Boundary conditions in general three-dimensional domains, submitted. Preprint available on arXiv:2011.11208.
(with Tak Kwong Wong) On the Well-posedness of Thin Layer Equations in Moving Domains, work in progress.
(with Xianpeng Hu) Global existence of solutions of multi-D incompressible MHD with discontinuous initial data, work in progress.
*Note: The papers on arXiv are NOT their final versions.
Listed in chronological order
Published or accepted:
27. (With Qasim Khan, Hassan Khan and Poom Kumam) Comparative analysis of fractional dynamical systems with various operators, AIMS Mathematics (2023), 8(6), pp. 13943–13983.
26. (With K.L. Cheung, K.P. Ho and T.L. Yee) Spherical Maximal Function on Local Morrey Spaces with Variable Exponents, Vietnam J. Math., Volume X (2022), Number X, XXXX–XXXX.
25. (with Susan Friedlander) On a class of forced active scalar equations with small diffusive parameters, Pure and Applied Functional Analysis 8(1) (2023), 215–241. Preprint available on arXiv:2011.08454.
24. Global regularity for the 3D compressible magnetohydrodynamics with general pressure, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 42 (2022), no. 6, pp. 2927-2943. Preprint available on arXiv:2012.02971.
23. Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure, Z. Angew. Math. Phys. (ZAMP) 73, 18 (2022).
22. Some Serrin type blow-up criteria for the three-dimensional viscous compressible flows with large external potential force, Math. Methods Appl. Sci, Vol. 45 (2022), no. 4, 2072-2086.
21. Existence, stability and long time behaviour of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force, J. Diff. Eqns, Vol. 299 (2021), 463-521.
20. (with Susan Friedlander) Correction to: Wellposedness and Convergence of Solutions to a Class of Forced Non-diffusive Equations with Applications, J. Math. Fluid Mech. 23 (2021), 81.
19. (with Susan Friedlander) Vanishing diffusion limits and long time behaviour of a class of forced active scalar equations, Arch. Rational Mechanics Ana. 240 (2021), no. 3, 1431–1485. Preprint available on arXiv:2005.10667.
18. (With K.L. Cheung, K.P. Ho and T.L. Yee) Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents, Mathematical Inequalities & Applications, Volume 23 (2020), Number 4, 1509–1528.
17. Existence and a blow-up criterion of solution to the 3D compressible Navier-Stokes-Poisson equations with finite energy, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 40 (2020), no. 3, 1775-1798.
16. Existence and uniqueness of low-energy weak solutions to the compressible 3D magnetohydrodynamics equations, J. Diff. Eqns, Vol. 268 (6) (2020), 2622-2671.
15. (with Susan Friedlander) Wellposedness and convergence of solutions to a class of forced non-diffusive equations with applications, J. Math. Fluid Mech. 21 (2019), 21-50. Preprint available on arXiv:1902.04366.
14. (With Susan Friedlander) Solutions to a class of forced drift-diffusion equations with applications to the magneto-geostrophic equations, Annals of PDE (2018), 4(2):14. Preprint available on arXiv:1705.06417.
13. (With K.L. Cheung) Existence and Uniqueness of Small Energy Weak Solution to multi- dimensional compressible Navier-Stokes Equations with Large External Potential Force, Journal of Mathematical Physics, Vol. 57 (2016), no. 8, 081513, pp. 1–19.
12. (with Tong Li) Existence of intermediate weak solution to the equations of three-dimensional chemotaxis systems, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 36 (2016), no. 2, pp. 861–875.
11. (with Susan Friedlander) Existence, uniqueness and regularity results for the viscous magneto-geostrophic equation, Nonlinearity, Vol. 28 (2015), no. 9, pp. 3193–3217. Preprint available on arXiv:1411.1980.
10. Corrigendum: A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 35 (2015), no. 3, 1387-1390.
9. (with Tong Li, Michael Winkler and Chuan Xue) Global small-data solutions of a two-dimensional chemotaxis system with rotational flux terms, Mathematical Models and Methods in Applied Sciences (M3AS), Vol. 25 (2015), no. 04, pp. 721–746.
8. (with Susan Friedlander) Holder continuity of solutions to the kinematic dynamo equations, J. Math. Fluid Mech. 16 (2014), 691-700. Preprint available on arXiv:1404.0691.
7. Existence of global weak solution to Navier-Stokes equations with large external potential force and general pressure, Math. Methods Appl. Sci., Vol. 37 (2014), no. 17, 2716-2727.
6. Global Solutions of the Navier-Stokes Equations for Isentropic Flow with Large External Potential Force, Z. Angew. Math. Phys. (ZAMP), Vol. 64 (2013), no. 3, 767-784.
5. A blow-up criterion for the 3D compressible magnetohydrodynamics in terms of density, Discrete and Continuous Dynamical Systems Series A (DCDS-A), Vol. 33 (2013), no. 8, 3791-3805.
4. (with David Hoff) Global low-energy weak solutions of the equations of 3D compressible magnetohydrodynamics, Arch. Rational Mechanics Ana. 205 (2012), no. 1, 27-58.
3. Nonexistence of self-similar singularities in the ideal viscoelastic flow, Electron. J. Diff. Equ., Vol. 2012 (2012), no. 93, 1-7.
2. Global low-energy weak solutions of the equations of 3D magnetohydrodynamics, Thesis (Ph.D.), Indiana University, 2012.
Survey on Heegaard Floer Homology, Thesis (M.Phil.), Chinese University of Hong Kong, 2007.
Preprints:
(With Susan Friedlander and Fei Wang) Ill/well-posedness of non-diffusive active scalar equations with physical applications, submitted. Preprint available on arXiv:2212.01835.
Uniqueness of weak solutions of the three-dimensional compressible Navier-Stokes equations with potential force. Preprint available on arXiv:2012.07028.
Large friction limit of the compressible Navier-Stokes equations with Navier Boundary conditions in general three-dimensional domains, submitted. Preprint available on arXiv:2011.11208.
(with Tak Kwong Wong) On the Well-posedness of Thin Layer Equations in Moving Domains, work in progress.
(with Xianpeng Hu) Global existence of solutions of multi-D incompressible MHD with discontinuous initial data, work in progress.
*Note: The papers on arXiv are NOT their final versions.
Some of my publications are listed on