Zu Chongzhi Mathematics Research Seminar

Date and Time (China standard time): Tuesday, December 3, 4:00 pm – 5:00 pm

Location: WDR 1007

Zoom: 946 7261 7215, Passcode: dkumath

Title: Norm inflation for incompressible fluids in supercritical Sobolev spaces

Speaker: Xiaoyutao Luo

Abstract: This talk focuses on the phenomenon illposedness of the 3D Euler and Navier-Stokes equations. We show that both two equations are illposed in supercritical Sobolev spaces $H^{s}$,  for any $0<s<\frac{5}{2} $ in the inviscid case and $0<s< \frac{1}{2} $ in the viscous case. The illposedness manifests as norm inflation: there are smooth initial data, arbitrarily small in $H^{s} $,  that become arbitrarily large in $H^{s}$ almost instantaneously.

Bio: I earned my Ph.D. in 2020 from the University of Illinois at Chicago. From 2020 to 2023, I was a postdoc at Duke University. Since the fall of 2023, I have been a faculty member at the Morningside Center of Mathematics, part of the Academy of Mathematics and Systems Science. My research focuses on partial differential equations (PDEs) arising in fluid dynamics.