Research

I study nonlinear partial differential equations, especially those arising from fluid dynamics and mathematical biology. The following is a list of my publications.

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

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

2. (with Francisco Gancedo, Rafa Granero-Belinchón, Elena Salguero, and Yao Yao) Infinite-in-Time Growth in Two-Phase Stokes-Transport System, preprint

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.