Nonlinear Partial Differential Equations

Date: September 28, 2021

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Tarek Elgindi, Duke University

Title: Remarks on the long-time behavior of 2d Euler flows

Abstract: We will discuss the issue of infinite-time filamentation of vorticity in 2d Euler flows. We establish a trichotomy that applies to all sufficiently regular steady states of the 2d Euler equation. Namely, it is either that a given steady state is unstable pointwise, or that it possesses a time-periodic flow map (i.e. it is isochronal), or that generic solutions starting nearby exhibit filamentation and grow at least linearly in C^1 as time grows to infinity. In a large class of important cases, we show that (at least) filamentation must occur. This is joint work with Theodore Drivas.