# Fudan International Seminar on Analysis, PDEs and Fluid mechanics

The speaker: Professor Andrej Zlatos (University of California, San Diego, USA)

Title of the talk: “Euler Equations on General Planar Domains”

Time: Thursday, 18 of November, 15:00 - 16:00.

Abstract: Bounded vorticity solutions to the 2D Euler equations on singular domains are typically not close to Lipschitz near boundary singularities, which makes their uniqueness a difficult open problem. I will present a general sufficient condition on the geometry of the domain that guarantees global uniqueness for all solutions initially constant near the boundary. This condition is only slightly more restrictive than exclusion of corners with angles greater than $\pi$ and, in particular, is satisfied by all convex domains. Its proof is based on showing that fluid particle trajectories for general bounded vorticity solutions cannot reach the boundary in finite time. The condition also turns out to be sharp in the latter sense: there are domains that come arbitrarily close to satisfying it and on which particle trajectories can reach the boundary in finite time.

ZOOM Id: 836 7313 8944

Passcode: 808818

We are pleased to inform you that the information on previous talks is available on the seminar web page

see PastTalks section

Organizing Committee: Professors Zhen Lei, Mikhail Korobkov, Adele Ferone, Remigio Russo, and Konstantin Pileckas

This seminar is organized by Fudan University (Shanghai, China) with the collaboration of Universita degli studi della Campania "Luigi Vanvitelli" (Caserta, Italy) and Vilnius University (Vilnius, Lithuania). This seminar is meant to gather renowned experts working on Geometric and Real Analysis with applications to PDEs and Mathematical Physics and represents an opportunity for presenting high-impact research, as well as facilitating the exchange of ideas between researchers.

2021-11-16

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