My research interests lie in the mathematical analysis of nonlinear deterministic and stochastic partial differential equations arising from fluid dynamics. In particular, I am interested in the well-posedness, ill-posedness, long-time dynamics, and finite-time singularity formation of PDEs.
I am in particularly interested in models from geophysics and electrohydrodynamics.
21. On the Three-dimensional Nernst-Planck-Boussinesq System (with Elie Abdo and Ruimeng Hu), to appear in Annals of PDE (2026).
20. Unveiling Traffic Wave of Linear Adaptive Cruise Control: A Second-order Macroscopic Traffic Flow Model (with Zihao Li, Fan Pu, Soyoung Ahn, Yunlong Zhang, Jiwan Jiang, and Yang Zhou), to appear in Transportation Research Part B: Methodological (2026).
19. Pathwise Solutions for Stochastic Hydrostatic Euler Equations under the Local Rayleigh Condition (with Ruimeng Hu), to appear in Journal of Evolution Equations (2026).
18. Coarsening Dynamics for the Burgers–Cahn–Hilliard System (with Peter Howard and Adam Larios), Physica D: Nonlinear Phenomena (2026). http://doi.org/10.1016/j.physd.2026.135271
17. On the Profile of Singularity Formation for the Incompressible Hydrostatic Boussinesq system (with Slim Ibrahim, Lingjun Qian, and Edriss S Titi), Nonlinearity (2026). https://doi.org/10.1088/1361-6544/ae5c52
16. Electroconvection in a Magnetic Field (with Elie Abdo, Peter Constantin, and Mihaela Ignatova), Discrete and Continuous Dynamical Systems (2026). https://doi.org/10.3934/dcds.2026023
15. Analysis and Numerical Approximation to Interactive Dynamics of Navier Stokes-Plate Interaction PDE System (with Pelin G Geredeli, Dylan Mcknight, and Mohammad Mahabubur Rahman), Commun. Nonlinear Sci. Numer. Simul. (2025). https://doi.org/10.1016/j.cnsns.2025.109489
14. On the local well-posedness of fractionally dissipated primitive equations with transport noise (with Ruimeng Hu and Rongchang Liu), Journal of Differential Equations (2025). https://doi.org/10.1016/j.jde.2025.113729
13. A new measure of coarseness for solutions to Cahn–Hilliard equations (with Peter Howard and Adam Larios), Nonlinearity (2025). https://doi.org/10.1088/1361-6544/ae1ee1
12. Regularization by noise for the inviscid primitive equations (with Ruimeng Hu and Rongchang Liu), Journal of Nonlinear Science (2025). https://doi.org/10.1007/s00332-025-10181-4
11. Estimation of Anisotropic Viscosities for the Stochastic Primitive Equations (with Igor Cialenco and Ruimeng Hu), Stoch PDE: Anal Comp. (2025). https://doi.org/10.1007/s40072-025-00363-2
10. Neural Network solutions to the critical SQG equations via approximating nonlocal periodic operators (with Elie Abdo and Ruimeng Hu), Physica D: Nonlinear Phenomena (2025). https://doi.org/10.1016/j.physd.2025.134652
9. Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise (with Rongchang Liu and Weinan Wang), Stochastic Processes and their Applications (2025). https://doi.org/10.1016/j.spa.2025.104603
8. Global existence for the stochastic Boussinesq equations with transport noise and small rough data (with Rongchang Liu and Weinan Wang), SIAM J. Math. Anal. (2024). https://doi.org/10.1137/23M155953
7. Higher-Order Error estimates for the Physics-Informed Neural Networks Approximating the Primitive Equations (with Ruimeng Hu, Alan Raydan, and Sui Tang), Partial Differ. Equ. Appl. (2023). https://doi.org/10.1007/s42985-023-00254-y
6. Stable Singularity Formation for the Inviscid Primitive Equations (with Charles Collot and Slim Ibrahim), Annales de l'Institut Henri Poincaré C, Analyse non linéaire (2023). https://doi.org/10.4171/AIHPC/87
5. On the Effect of Fast Rotation and Vertical Viscosity on the Lifespan of the 3D Primitive Equations (with Xin Liu and Edriss S. Titi), J. Math. Fluid Mech. (2022). https://link.springer.com/article/10.1007/s00021-022-00705-3
4. Local Martingale Solutions and Pathwise Uniqueness for the Three-dimensional Stochastic Inviscid Primitive Equations (with Ruimeng Hu), Stoch PDE: Anal Comp. (2022). https://doi.org/10.1007/s40072-022-00266-6
3. On the Effect of Rotation on the Life-span of Analytic Solutions to the 3D Inviscid Primitive Equations (with Tej-Eddine Ghoul, Slim Ibrahim, and Edriss S. Titi), Arch. Ration. Mech. Anal. (2022). https://doi.org/10.1007/s00205-021-01748-y
2. Finite-time Blowup and Ill-posedness in Sobolev Spaces of the Inviscid Primitive Equations with Rotation (with Slim Ibrahim and Edriss S. Titi), J. Differ. Equ. (2021). https://doi.org/10.1016/j.jde.2021.03.037
1. On the Well-posedness of Reduced 3D Primitive Geostrophic Adjustment Model with Weak Dissipation (with Chongsheng Cao and Edriss S. Titi), J. Math. Fluid Mech. (2020). https://doi.org/10.1007/s00021-020-00495-6
4. Well-posedness and ill-posedness of the primitive equations with fractional horizontal dissipation (with Elie Abdo and Changhui Tan), submitted, arXiv:2508.12883 (2025).
3. Averaging principle for the stochastic primitive equations in the large rotation limit (with Rongchang Liu and Vincent Martinez), submitted, arXiv:2503.00991 (2025).
2. On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains (with Elie Abdo), submitted, arXiv:2409.05209 (2024).
1. On the Long-time Dynamics and Ergodicity of the Stochastic Nernst-Planck-Navier-Stokes System (with Elie Abdo and Ruimeng Hu), submitted, arXiv: 2310.20484 (2023).