Listed by research areas
Listed by research areas
Published or accepted:
Active scalar equations:
(With Qasim Khan and Bao Quoc Tang) Existence, asymptotic behaviour and convergence of a generalised 3D Muskat problem in stable regime, to appear in Advances in Nonlinear Analysis. Preprint available on arXiv:2603.16172
(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.
Euler equations:
(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, to appear in SIAM Journal on Mathematical Analysis.
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 Hongli An, Engui Fan and Manwai Yuen) Integrable Ermakov structure, time-periodic vortex solutions and nonlinear Schrödinger connection in the transverse magnetohydrodynamic equations, Physica D: Nonlinear Phenomena, Vol. 492 (2026).
(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:
(With Hongli An, Ziliang Li and Manwai Yuen) On the compressible Navier-Stokes equation with Coriolis force and density-dependent viscosity: The Cartesian vector solutions and their properties, Commun. Theor. Phys. 78 055001 (2026).
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) Modified approach for linear and non-linear IBVPs with fractional dynamics, Communications in Nonlinear Science and Numerical Simulation, Volume 163, Part 2, (2026), 110500.
(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, Math Ed Res J 38, 485–509 (2026).
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.
Submitted:
(With Salman Ahmad, Muhammad Bilal, Salman Zeb, Zafar Hayat Khan and Hengjie Guo) A Critical Study of Mathematical Frameworks for the Thermophysical Characterization of Nanoparticles, submitted.
(With Hongli An and Zheng Liu) On the classification and dynamical properties of vector rogue waves for the complex Kraenkel-Manna-Merle system in circularly polarized ferrites, submitted.
(With Susan Friedlander) Long time dynamics and anomalous dissipation of energy in viscous forced active scalar equations, submitted.
(With Qasim Khan) Performance and precision of He's and Daftardar-Jafari polynomials in nonlinear fractional PDEs, submitted.
(With Qasim Khan) Computational efficiency on solving Schrodinger equations with various normalization functions, submitted.
(With Ning-An Lai and Wei Xu) Lifespan for the ideal compressible magnetohydrodynamics with a vertical magnetic field in R^2, submitted.
(With Ning-An Lai and Wei Xu) Enhanced lifespan to the one and a half dimensional inviscid rotating shallow water system, submitted.
(With Hongli An, Engui Fan and Manwai Yuen), Airy asymptotics for the high-order derivative nonlinear Schrödinger equation on the line, submitted.
(With Yuxuan Lu and Xin Zhong) Global weak solutions of compressible Navier-Stokes-Poisson equations with discontinuous initial data and vacuum, submitted.
(With Xin Zhong) Large friction limit of compressible Navier-Stokes equations with Navier boundary conditions in a half-space, submitted. Preprint available on arXiv:2011.11208v2.
Work in progress:
(With Vincent Martinez) Local well-posedness for the generalized MG equation in critical L^2-based Besov spaces, work in progress.
(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.
(With Longjin Lv, Sen Wong and Manwai Yuen) On Lifespan Estimates of Classical Solutions to Non-isentropic Isothermal Compressible Euler Equations in R^N, work in progress.
(With Yiru Pei and Kin Keung Poon) Effect of Flipped Classroom Learning Environments on Secondary Students’ Geometry Learning: A Case Study Using Congruent Triangles, work in progress.
(With Yiru Pei and Kin Keung Poon) Computational efficiency on solving multi dimensional non-linear dynamical systems under different polynomials, work in progress.
*Note: The papers on arXiv are NOT their final versions.
Published or accepted:
38. (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, to appear in SIAM Journal on Mathematical Analysis.
37. (With Qasim Khan and Bao Quoc Tang) Existence, asymptotic behaviour and convergence of a generalised 3D Muskat problem in stable regime, to appear in Advances in Nonlinear Analysis. Preprint available on arXiv:2603.16172
36. (With Qasim Khan) Modified approach for linear and non-linear IBVPs with fractional dynamics, Communications in Nonlinear Science and Numerical Simulation, Volume 163, Part 2, (2026), 110500.
35. (With Hongli An, Engui Fan and Manwai Yuen) Integrable Ermakov structure, time-periodic vortex solutions and nonlinear Schrödinger connection in the transverse magnetohydrodynamic equations, Physica D: Nonlinear Phenomena, Vol. 492 (2026).
34. (With Hongli An, Ziliang Li and Manwai Yuen) On the compressible Navier-Stokes equation with Coriolis force and density-dependent viscosity: The Cartesian vector solutions and their properties, Commun. Theor. Phys. 78 055001 (2026).
33. (With Yiru Pei and Kin Keung Poon) The influence of mathematics anxiety on mathematics performance: The mediating effect of mathematical engagement, Math Ed Res J 38, 485–509 (2026).
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.
Submitted:
(With Salman Ahmad, Muhammad Bilal, Salman Zeb, Zafar Hayat Khan and Hengjie Guo) A Critical Study of Mathematical Frameworks for the Thermophysical Characterization of Nanoparticles, submitted.
(With Hongli An and Zheng Liu) On the classification and dynamical properties of vector rogue waves for the complex Kraenkel-Manna-Merle system in circularly polarized ferrites, submitted.
(With Susan Friedlander) Long time dynamics and anomalous dissipation of energy in viscous forced active scalar equations, submitted.
(With Qasim Khan) Performance and precision of He's and Daftardar-Jafari polynomials in nonlinear fractional PDEs, submitted.
(With Qasim Khan) Computational efficiency on solving Schrodinger equations with various normalization functions, submitted.
(With Ning-An Lai and Wei Xu) Lifespan for the ideal compressible magnetohydrodynamics with a vertical magnetic field in R^2, submitted.
(With Ning-An Lai and Wei Xu) Enhanced lifespan to the one and a half dimensional inviscid rotating shallow water system, submitted.
(With Hongli An, Engui Fan and Manwai Yuen), Airy asymptotics for the high-order derivative nonlinear Schrödinger equation on the line, submitted.
(With Yuxuan Lu and Xin Zhong) Global weak solutions of compressible Navier-Stokes-Poisson equations with discontinuous initial data and vacuum, submitted.
(With Xin Zhong) Large friction limit of compressible Navier-Stokes equations with Navier boundary conditions in a half-space, submitted. Preprint available on arXiv:2011.11208v2.
(With Longjin Lv, Sen Wong and Manwai Yuen) On Lifespan Estimates of Classical Solutions to Non-isentropic Isothermal Compressible Euler Equations in R^N, submitted.
Work in progress:
(With Vincent Martinez) Local well-posedness for the generalized MG equation in critical L^2-based Besov spaces, work in progress.
(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.
(With Longjin Lv, Sen Wong and Manwai Yuen) On Lifespan Estimates of Classical Solutions to Non-isentropic Isothermal Compressible Euler Equations in R^N, work in progress.
(With Yiru Pei and Kin Keung Poon) Effect of Flipped Classroom Learning Environments on Secondary Students’ Geometry Learning: A Case Study Using Congruent Triangles, work in progress.
(With Yiru Pei and Kin Keung Poon) Computational efficiency on solving multi dimensional non-linear dynamical systems under different polynomials, work in progress.
*Note: The papers on arXiv are NOT their final versions.
Some of my publications are listed on