Research

Fluid Models

• On the global stability for the 3D incompressible MHD equations with anisotropic dissipation (with Wen Feng and Jiahong Wu), submitted, 2025. 

• Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces (with Zachary Bradshaw), Proceedings of the American Mathematical Society, 153 (2025), no. 9, pp. 3867-3881.

• On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions (with Elie Abdo**), Applicable Analysis, 103 (2024), no. 16, 3017-3028.

• Stability for a system of the 2D incompressible MHD equations with fractional dissipation (with Wen Feng and Jiahong Wu), Journal of Mathematical Fluid Mechanics, 26 (2024), no. 4, paper no. 57.

• On the global well-posedness and analyticity of some electrodiffusion models in ideal fluids and porous media (with Elie Abdo** and Fizay-Noah Lee**), SIAM Journal on Mathematical Analysis, 55 (2023), no. 6, 6838-6866.

• Nonlinear stability for the 2D  incompressible MHD system with fractional dissipation in the horizontal direction (with Wen Feng and Jiahong Wu), Journal of Evolution Equations, 23 (2023), no. 2, paper No. 32, 37 pp.

• Quantitative bounds of critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces (with Wen Feng and Jiao He), submitted, 2022.

• On the analyticity and Gevrey regularity of solutions to the three-dimensional inviscid Boussinesq equations in a half space. Communications in Mathematical Sciences, 20 (2022), no. 2, 479-493.

• Global existence and stability for the 2D Oldroyd-B model with mixed partial dissipation (with Wen Feng and Jiahong Wu), Proceedings of the American Mathematical Society, 150 (2022), no. 12, 5321-5334.

• On the global stability of large solutions for the 3D Boussinesq equations with Navier boundary conditions, Archiv der Mathematik, 116 (2021), no. 4, 445-456.

• Norm inflation for the Boussinesq system (with Zongyuan Li), Discrete and Continuous Dynamical Systems-B, 26 (2021), no. 10, 5449-5463.

• Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity (with Igor Kukavica), Pure and Applied Functional Analysis, 5 (2020), no. 1, 27-45. 

• Long time behavior of the solutions to the 2D Boussinesq equations without diffusivity (with Igor Kukavica), Journal of Dynamics and Differential Equations, 32 (2020), no. 4, 2061-2077.

• On the global regularity for a 3D Boussinesq model without thermal diffusion, Zeitschrift für Angewandte Mathematik und Physik, 70 (2019), no. 6, paper 174.

Inverse Problems

• On a partial data inverse problem for the semi-linear wave equations (with Boya Liu), submitted, 2025. 

• A Calderón type inverse problem for the active scalar equations with fractional dissipation (with Li Li), Inverse Problems & Imaging, (Publisher Early Access), 2025.

• An inverse problem for fractional drift-diffusion equations with potentials, submitted, 2025. 

• Quantitative unique continuation for Robin boundary value problems on $C^{1, 1}$ domains (with Zongyuan Li), Indiana University Mathematics Journal, 72 (2023), no. 4, 1429-1460.

Mathematical Biology and Optimal Control

• A compartmental model for epidemiology with human behavior and stochastic effects (with Christian Parkinson), Mathematical Biosciences, 392 (2026), paper No. 109588.

• Optimal control in SIR models with noncompliance as a social contagion (with Chloe Ngo* and Christian Parkinson), submitted, 2025. 

• Optimal control of a reaction-diffusion epidemic model with noncompliance (with Marcelo Bongarti and Christian Parkinson), European Journal of Applied Mathematics, (Publisher Early Access), 2025.

• Analysis of a reaction-diffusion SIR epidemic model with noncompliant behavior (with Christian Parkinson), SIAM Journal on Applied Mathematics, 82 (2023), no. 5, 1969-2002.

Kinetic Models

• On the axi-symmetric solutions to the Landau-Fermi-Dirac equations, submitted, 2025. 

• A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation (with Christopher Henderson and Giacomo Lucertini**), submitted, 2024.  

• Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation (with Christopher Henderson), Discrete and Continuous Dynamical Systems, 44 (2024), no. 4, 1026-1072.

• Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data (with Christopher Henderson), SIAM Journal on Mathematical Analysis, 53 (2022), no. 3, 2845-2875.

Stochastic Processes

• Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise (with Quyuan Lin and Rongchang Liu), Stochastic Processes and their Applications, 184 (2025), paper no. 104603.

• Global existence for the stochastic Boussinesq equations with transport noise and small rough data (with Quyuan Lin and Rongchang Liu), SIAM Journal on Mathematical Analysis, 56 (2024), no. 1, 501-528.

• Almost sure existence of global weak solutions to the Boussinesq equations (with Haitian Yue), Dynamics of PDEs, 17 (2020), no. 2, 165-183.