Research

I am interested in applied mathematics and analysis of partial differential equations (PDEs).

Fluid & Kinetic Models

** denotes a graduate student author

*** denotes a postdoc research mentee

Fluid models, including the Navier-Stokes equations, the Oldroyd-B (visco-elastic) system, the magneto-hydrodyamics (MHD) equations, the porous medium equations, and the fractional Boussinesq equations

On the well-posedness and stability for some fluid equations (with X. Xu***), in preparation, 2025.
Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces (with Z. Bradshaw), Proc. Amer. Math. Soc., 153 (2025), no. 9, pp. 3867-3881.
On the global stability for the 3D incompressible MHD equations with anisotropic dissipation (with W. Feng and J. Wu), submitted, 2025.
Stability for a system of the 2D incompressible MHD equations with fractional dissipation (with W. Feng and J. Wu), J. Math. Fluid Mech., 26 (2024), no. 4, paper no. 57.
On the space-time analyticity of the inhomogeneous heat equation on the half space with Neumann boundary conditions (with E. Abdo**), Appl. Anal., 103 (2024), no. 16, 3017-3028.
On the global well-posedness and analyticity of some electrodiffusion models in ideal fluids and porous media (with E. Abdo** and F-N. Lee**), SIAM J. Math. Anal., 55 (2023), no. 6, 6838-6866.
Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction (with W. Feng and J. Wu), J. Evol. Equ., 23 (2023), no. 2, paper No. 32, 37 pp.
On the analyticity and Gevrey regularity of solutions to the three-dimensional inviscid Boussinesq equations in a half space, Commun. Math. Sci., 20 (2022), no. 2, 479-493.
Global existence and stability for the 2D Oldroyd-B model with mixed partial dissipation (with W. Feng and J. Wu), Proc. Amer. Math. Soc., 150 (2022), no. 12, 5321-5334.
Quantitative bounds of critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces (with W. Feng and J. He), submitted, 2022.
On the global stability of large solutions for the 3D Boussinesq equations with Navier boundary conditions, Arch. Math. (Basel), 116 (2021), no. 4, 445-456.
Norm inflation for the Boussinesq system (with Z. Li), Discrete Contin. Dyn. Syst. Ser. B, 26 (2021), no. 10, 5449-5463.
Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity (with I. Kukavica), Pure Appl. Funct. Anal., 5 (2020), no. 1, 27-45.
Long time behavior of the solutions to the 2D Boussinesq equations without diffusivity (with I. Kukavica), J. Dynam. Differential Equations, 32 (2020), no. 4, 2061-2077.
On the global regularity for a 3D Boussinesq model without thermal diffusion, Z. Angew. Math. Phys., 70 (2019), no. 6, paper 174.

Kinetic equations, including regularity, existence, and uniqueness of solutions to Boltzmann and Landau equations, and kinetic Fokker-Planck equations, especially with boundary effects

A kinetic Nash inequality and precise boundary behavior of the kinetic Fokker-Planck equation (with C. Henderson and G. Lucertini**), submitted, 2024.
Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation (with C. Henderson), Discrete Contin. Dyn. Syst., 44 (2024), no. 4, 1026-1072.
Local well-posedness for the Boltzmann equation with very soft potential and polynomially decaying initial data (with C. Henderson), SIAM J. Math. Anal., 53 (2022), no. 3, 2845-2875.

Applied Mathematics & Interdisciplinary Research

* denotes an undergraduate student author

Mathematical biology and population dynamics, incorporating social contagion theory, optimal control, public health analysis, epidemiological modeling, human behavior, stochastic effects, and data-driven problems

A data-driven approach for the optimal control problem of the SEIRV model (with A. Ganguly*), in preparation, 2025.
On the stochastic SIR model with truncated Levy flights, (with C. Parkinson and C. Wang), in preparation, 2025.
Optimal control in SIR models with noncompliance as a social contagion (with C. Ngo* and C. Parkinson), submitted, 2025.
Optimal control of a reaction-diffusion epidemic model with noncompliance (with M. Bongarti and C. Parkinson), European J. Appl. Math., (Early Access) pp 1-26, doi: 10.1017/S0956792525000130, 2025.
A compartmental model for epidemiology with human behavior and stochastic effects (with C. Parkinson), under revision at Math. Biosci., 2025.
Analysis of a reaction-diffusion SIR epidemic model with noncompliant behavior (with C. Parkinson), SIAM J. Appl. Math., 82 (2023), no. 5, 1969-2002.

Inverse problems and unique continuation, including parameter estimation, geometric inverse problems, partial data problem, and unique continuation

On an inverse problem for the incompressible Navier-Stokes equations (with B. Liu and Y. Zhang), in preparation, 2025.
On an inverse problem for the semi-linear wave equations with partial data (with B. Liu), preprint, 2025.
A Calderón type inverse problem for the active scalar equations with fractional dissipation (with L. Li), Inverse Probl. Imaging, (Early Access) doi: 10.3934/ipi.2025044 , 2025.
Quantitative unique continuation for Robin boundary value problems on C^{1, 1} domains (with Z. Li), Indiana Univ. Math. J., 72 (2023), no. 4, 1429-1460.

Stochastic processes, including applications in bio-chemistry, modeling of electro-membrane processes, the transport-type noise, regularization and smoothing effects, and random initial data in SPDEs

Global well-posedness and enhanced dissipation for the 2D stochastic Nernst-Planck-Navier-Stokes equations with transport noise (with Q. Lin and R. Liu), Stochastic Process. Appl., 184 (2025), paper no. 104603, 22 pp.
Global existence for the stochastic Boussinesq equations with transport noise and small rough data (with Q. Lin and R. Liu), SIAM J. Math. Anal., 56 (2024), no. 1, 501-528.
Almost sure existence of global weak solutions to the Boussinesq equations (with H. Yue), Dyn. Partial. Differ. Equ., 17 (2020), no. 2, 165-183.

Page updated

Google Sites

Report abuse