Mathematics Colloquium
Tarek M. Elgindi
Duke University
Title: Some aspects of the long-time behavior of 2d fluid flows
Date: Friday, October 18th, 2024
Place and Time: Love 101, 3:05-3:55 pm
Abstract. We will discuss several aspects of steady solutions to the 2d incompressible Euler equation. We will discuss flexibility and rigidity of steady Euler flows and their link to solutions of semilinear elliptic equations. We will then move to discuss their stability properties and how they can be used to establish some non-trivial dynamical behavior, such as filamentation, for unsteady solutions. In particular, we will discuss the concept of twisting, its stability, and various consequences thereof. This is based on joint works with several co-authors, including M. Coti-Zelati, T. Drivas, Y. Huang, I. Jeong, A. Said, K. Widmayer, and C. Xie.