Zu Chongzhi Distinguished Lecture

Date and Time (China standard time): Friday, June 20, 9:00 am – 10:00 am

Location: WDR 1007

Zoom: 998 8039 9161, Passcode: dkumath

Title: Local regularity and finite time blow-up for the generalized SQG equation on the half-plane

Speaker: Andrej Zlatos

Abstract: The generalized SQG equation with parameter $\alpha\in(0,\frac 12)$ interpolates between the 2D Euler and SQG equations, for which $\alpha=0$ and $\alpha=\frac 12$, respectively.  We show that this PDE with $alpha\le \frac 14$ is locally well-posed on the half-plane in spaces of bounded integrable locally Lipschitz functions that are natural for its dynamic on domains with boundaries, and allow for some power growth of the derivative in the normal direction at the boundary.  We also show existence of solutions exhibiting finite time blow-up in this whole local well-posedness parameter regime, which is the first finite time singularity result for equations (as opposed to patch models) of this type.  Moreover, we prove sharpness of both these results by showing ill-posedness of the PDE in the above spaces when $\alpha>\frac 14$.

Bio: Andrej Zlatos obtained his PhD. from Caltech in 2003, after which he held faculty positions at the University of Chicago and the University of Wisconsin.  Since 2016 he has been a professor at the University of California San Diego.  He works in the area of partial differential equations, specializing in fluid dynamics, reaction-diffusion equations, and mixing.  He is an author of over 60 mathematical papers, as well as a recipient of the Sloan Fellowship and the Simons Fellowship.