Listed by research areas
Listed by research areas
Published or accepted:
Active scalar equations:
(With Susan Friedlander and Fei Wang) Ill/well-posedness of non-diffusive active scalar equations with physical applications, J. Diff. Eqns, Vol. 411 (2024), 880-902. Preprint available on arXiv:2212.01835.
(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 K.L. Cheung, K.P. Ho and T.L. Yee) Spherical Maximal Function on Local Morrey Spaces with Variable Exponents, Vietnam J. Math., Volume 52 (2024), 107–115.
(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) Hölder continuity of solutions to the kinematic dynamo equations, J. Math. Fluid Mech. 16 (2014), 691-700. Preprint available on arXiv:1404.0691.
Magnetohydrodynamics equations:
(With Lv Cai, Ning-An Lai and Manwai Yuen) Liouville-type theorems for the stationary ideal magnetohydrodynamics equations in R^n, J. Math. Fluid Mech. 26 (2024), 65.
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.
Numerical methods:
(With Qasim Khan), Iterative procedure for non-linear fractional integro-differential equations via Daftardar–Jafari polynomials, Partial Differential Equations in Applied Mathematics, Volume 14, (2025), 101167.
(With Qasim Khan and Hassan Khan) Application of an efficient analytical technique based on Aboodh transformation to solve linear and non-linear dynamical systems of integro-differential equations, Partial Differential Equations in Applied Mathematics, Volume 11, (2024), 100848.
(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.
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.
Reaction-diffusion equations:
(With Qasim Khan and Bao Quoc Tang), Turing Instability Suppressed and Induced by Multiplicative Noise in Brusselator System, Communications in Nonlinear Science and Numerical Simulation, Volume 151, (2025), 109092.
Viscoelastic flow:
Nonexistence of self-similar singularities in the ideal viscoelastic flow, Electron. J. Diff. Equ., Vol. 2012 (2012), no. 93, 1-7.
Mathematics education:
(With Yiru Pei and Kin Keung Poon) The influence of mathematics anxiety on mathematics performance: The mediating effect of mathematical engagement, to appear in Mathematics Education Research Journal.
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:
(With Ning-An Lai and Wei Xu) Enhanced lifespan to the one and a half dimensional inviscid rotating shallow water system, submitted.
(With Ning-An Lai and Wei Xu) A Hardy type inequality in R^2 and its application to the Euler equation with non-zero vorticity, submitted.
(With Yiru Pei and Kin Keung Poon) Effect of Flipped Classroom Learning Environments on Secondary Students’ Geometry Learning: A Case Study Using Congruent Triangles, submitted.
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.
Published or accepted:
33. (With Yiru Pei and Kin Keung Poon) The influence of mathematics anxiety on mathematics performance: The mediating effect of mathematical engagement, to appear in Mathematics Education Research Journal.
32. (With Qasim Khan and Bao Quoc Tang), Turing Instability Suppressed and Induced by Multiplicative Noise in Brusselator System, Communications in Nonlinear Science and Numerical Simulation, Volume 151, (2025), 109092.
31. (With Qasim Khan), Iterative procedure for non-linear fractional integro-differential equations via Daftardar–Jafari polynomials, Partial Differential Equations in Applied Mathematics, Volume 14, (2025), 101167.
30. (With Lv Cai, Ning-An Lai and Manwai Yuen) Liouville-type theorems for the stationary ideal magnetohydrodynamics equations in R^n, J. Math. Fluid Mech. 26 (2024), 65.
29. (With Susan Friedlander and Fei Wang) Ill/well-posedness of non-diffusive active scalar equations with physical applications, J. Diff. Eqns, Vol. 411 (2024), 880-902. Preprint available on arXiv:2212.01835.
28. (With Qasim Khan and Hassan Khan) Application of an efficient analytical technique based on Aboodh transformation to solve linear and non-linear dynamical systems of integro-differential equations, Partial Differential Equations in Applied Mathematics, Volume 11, (2024), 100848.
27. (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 52 (2024), 107–115.
26. (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.
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) Hölder 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 Ning-An Lai and Wei Xu) Enhanced lifespan to the one and a half dimensional inviscid rotating shallow water system, submitted.
(With Ning-An Lai and Wei Xu) A Hardy type inequality in R^2 and its application to the Euler equation with non-zero vorticity, submitted.
(With Yiru Pei and Kin Keung Poon) Effect of Flipped Classroom Learning Environments on Secondary Students’ Geometry Learning: A Case Study Using Congruent Triangles, submitted.
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.
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