Research

I am broadly interested in the study of nonlinear partial differential equations, especially those arising from fluid dynamics, plasma physics, and mathematical biology. 

In the study of fluid dynamics, I have been interested in the stable/unstable phenomena, especially in the context of free-boundary fluid problems. Stable and unstable phenomena are ubiquitous in many types of fluids, including both gas and liquid. For example, the gravity is able to de-stablize two immiscible liquid one the lighter one sits above the heavier one; the bulk of water might display quite complicated dynamics when vorticity is created, signaling a strong instability. I am particularly interested in quantitatively and rigorously studying those phenomena.

In the study of plasma physics, I am interested in understanding magnetic reconnection, a fundamental physical process in electrically conducting plasmas where opposing magnetic field lines snap, break, and re-fuse into a new configuration. Magnetic reconnection usually occurs in the formation of solar flares and coronal mass ejections. While it has been understood that such phenomenon is triggered by magnetic diffusivity, recent research also suggests magnetic reconnection happen in an ideal setting i.e. when magnetic diffusivity is absent. My work has been focused on building rigorous mathematical theory concerning such ''ideal magnetic reconnection.''

In the study of mathematical biology, I have been working on the Patlak-Keller-Segel equations, which classically model chemotaxis. In short, chemotaxis is a biological phenomena which describe the evolution of cells/bateria in response to certain external chemicals. I am particularly interested in this phenomenon when one takes the effect of incompressible fluid into account. Such fluid-chemotaxis interaction brings extremely rich dynamics.

The following is a list of my publications.

Unstable Phenomena in Incompressible free-boundary fluids

1. (with Jungkyoung Na, and Jia Shi) On Two-Phase Stokes-Transport System, in preparation

2. (with Francisco Gancedo, Rafa Granero-Belinchón, Elena Salguero, and Yao Yao) Unstable Interface Dynamics for Gravity Stokes Flow, preprint (2026). https://arxiv.org/abs/2601.18460.

3. Exponential Vorticity Hessian Growth in Capillary Liquid Drop in Two Dimensions, preprint (2025). https://arxiv.org/abs/2506.11414, to appear in Nonlinearity

4. (with Chenyun Luo and Yao Yao) Small scale creation for 2D free boundary Euler equations with surface tension, Ann. PDE, 10, 13 (2024). https://doi.org/10.1007/s40818-024-00179-8.

Magnetohydrodynamics and Plasma Physics

1. (with Peter Constantin) Electric inertia and ideal magnetic reconnection in 2D, preprint (2026). https://arxiv.org/abs/2604.15568

2. (with Lydia Boubendir, Peter Constantin, and Hezekiah Grayer II) On Ideal Magnetic Reconnection, in preparation

Stable Phenomena in Compressible Fluid Dynamics

1. (with Marcelo M. Disconzi and Chenyun Luo) On a class of global solutions to 3D free-boundary relativistic Euler equations with a physical vacuum boundary, preprint (2026). https://arxiv.org/abs/2601.15010.

2. (with Marcelo M. Disconzi, Chenyun Luo, and Jared Speck) On Relativistic Stars, in preparation

Regularity and Blowup Suppression of Chemotaxis

1. (with Elie Abdo) On the space-time analyticity of the Keller-Segel-Navier-Stokes system, J Nonlinear Sci 35, 62 (2025). https://doi.org/10.1007/s00332-025-10158-3

2. Suppression of Chemotactic Singularity via Viscous Flow with Large Buoyancy, SIAM J. Math. Anal., 56, 6 (2024). https://doi.org/10.1137/24M1669001

3. (with Alexander Kiselev) Suppression of chemotactic blowup by strong buoyancy in Stokes-Boussinesq flow with cold boundary, J. Funct. Anal., 287, 7 (2024). https://doi.org/10.1016/j.jfa.2024.110541.

4. (with Alexander Kiselev and Yao Yao) Suppression of chemotactic singularity by buoyancy, Geom. Funct. Anal. (2025). https://doi.org/10.1007/s00039-025-00706-0