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.
Well-posedness and ill-posedness of the primitive equations with fractional horizontal dissipation (with Elie Abdo and Changhui Tan), submitted, arXiv:2508.12883 (2025).
Electroconvection in a Magnetic Field (with Elie Abdo, Peter Constantin, and Mihaela Ignatova), submitted, arXiv:2508.07439 (2025).
Analysis and Numerical Approximation to Interactive Dynamics of Navier Stokes-Plate Interaction PDE System (with Pelin G Geredeli, Dylan Mcknight, and Mohammad Mahabubur Rahman), submitted, arXiv:2507.02230 (2025).
Averaging principle for the stochastic primitive equations in the large rotation limit (with Rongchang Liu and Vincent Martinez), submitted, arXiv:2503.00991 (2025).
On the Dirichlet Fractional Laplacian and Applications to the SQG Equation on Bounded Domains (with Elie Abdo), submitted, arXiv:2409.05209 (2024).
Comparison of Coarsening Dynamics for the Cahn--Hilliard and Burgers--Cahn--Hilliard Equations (with Peter Howard and Adam Larios), submitted, arXiv:2405.11709 (2024).
On the Three-dimensional Nernst-Planck-Boussinesq System (with Elie Abdo and Ruimeng Hu), submitted, arXiv: 2405.02152 (2024).
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).
Pathwise Solutions for Stochastic Hydrostatic Euler Equations and Hydrostatic Navier-Stokes Equations Under the Local Rayleigh Condition (with Ruimeng Hu), submitted, arXiv:2301.07810 (2023).
On the local well-posedness of fractionally dissipated primitive equations with transport noise (with Ruimeng Hu and Rongchang Liu), to appear in Journal of Differential Equations, arXiv:2501.09956 (2025).
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
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
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
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
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
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
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
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
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
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
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
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