Zu Chongzhi Research Seminar

Date and Time (China standard time): Friday, December 12, 10:00 am – 11:00 am

Location: WDR 1007

Zoom: 974 8661 5780, Passcode: dkumath

Title: Spacetime decay of mild solutions and conditional quantitative transfer of regularity of the incompressible Navier-Stokes Equations

Speaker: Xiangxiang Su, Shanghai Jiao Tong University

Abstract: We discuss the “transfer of regularity” phenomenon for the incompressible Navier–Stokes Equations (NSE) in dimension $n \geq 3$; that is, the strong solutions of NSE on $\mathbb{R}^n$ can be nicely approximated by those on sufficiently large domains $\Omega \subset \mathbb{R}^n$ under the no-slip boundary condition. Based on the spacetime decay estimates for mild solutions of NSE established by Miyakawa and Schonbek, etc., we obtain quantitative estimates on higher-order derivatives of velocity and pressure for the incompressible Navier–Stokes flow on large domains under certain additional smallness assumptions of the Stokes’ system and/or the initial velocity, thus complementing the transfer of regularity theorems obtained by Robinson (Nonlinearity 2021) and O\.z\’anski (J. Math. Fluid Mech. 2021). 

Joint work with Siran Li (Shanghai Jiao Tong University)

Bio: Xiangxiang Su is a Postdoctoral Researcher at the School of Mathematical Sciences, Shanghai Jiao Tong University. She received her Ph.D. in Mathematics from Shanghai Jiao Tong University in 2025, under the supervision of Prof. Feng Xie. Her research interests lie in partial differential equations  arising in mathematical physics and geometry, particularly in fluid dynamics, phase transition models, and isometric immersions. Her work has appeared in journals such as Archive for Rational Mechanics and Analysis, Science China Mathematics, and Chinese Annals of Mathematics, Series B.