Research

My general research interests lie in partial differential equations (PDEs), especially the mathematical analysis of the Euler, Navier-Stokes, and other equations arising from fluid dynamics. My work primarily focuses on (i) well-posedness and (ii) long-time dynamics, with an emphasis on understanding the mechanisms that stabilize or destabilize fluid flows.

Publications

Preprints

[3]. (with Rajendra Beekie, Hao Jia) Optimal inviscid damping and vorticity depletion for non-monotonic shear flows, arXiv:2610.08912 (2026).

Journal articles

[2]. (with Rajendra Beekie, Hao Jia) Uniform vorticity depletion and inviscid damping for periodic shear flows in the high Reynolds number regime, Arch Rational Mech Anal 250, 7 (2026).

[1]. (with Zixiao Liu) Asymptotic behavior of positive solutions of some nonlinear elliptic equations on cylinders, Journal of Differential Equations, 401 (2024).

Talks and Presentations

• Optimal inviscid damping and vorticity depletion for general non-monotonic shear flows, 2026 Fall AMS Western Sectional Meeting, Arizona State University, Tempe, AZ, November 2026 (Abstract)

• Resolvent estimates for hydrodynamic stability in the high Reynolds number regime, 2026 Fall AMS Western Sectional Meeting, Arizona State University, Tempe, AZ, November 2026 (Abstract)

• Uniform inviscid damping and vorticity depletion near non-monotonic shear flows, poster, International Congress of Mathematicians (2026), Philadelphia, PA, July 2026 (Poster)

• Hydrodynamic stability near shear flows, Pitt AWM Student Seminar, Online, February 2026

• Hydrodynamic stability near shear flows, Math colloquium talk, University of Minnesota Duluth, Duluth, MN, November 2025

• Uniform vorticity depletion and inviscid damping near non-monotonic shear flows, 2025 Fall AMS Southeastern Sectional Meeting, Tulane University, New Orleans, LA, October 2025 (Abstract)

• Linear inviscid damping and vorticity depletion for shear flows, Math Seminar, Beijing Normal University, Beijing, China, January 2024 (Abstract)