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), Transportation Research Part B: Methodological (2026). https://doi.org/10.1016/j.trb.2026.103506
19. Pathwise Solutions for Stochastic Hydrostatic Euler Equations under the Local Rayleigh Condition (with Ruimeng Hu), Journal of Evolution Equations (2026). https://doi.org/10.1007/s00028-026-01233-7
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).