Research

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

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 considering this phenomenon when one takes the effect of incompressible fluid in account, which brings rich and interesting dynamics.

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.

The following is a list of my publications.

Stability and Instability in free-boundary fluids

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 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.

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.

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