Alexander Kiselev : Nonlocal maiximum principles for active scalars

Posted by Alexey Cheskidov , part of the Departmental Colloquium.

At

March 4, 2011, 3 p.m.

In

SEO 636

Abstract

Active scalars appear in many problems of fluid dynamics. The most common examples of active scalar equations include 2D Euler equation describing two-dimensional flow of ideal fluid, surface quasi-geostrophic equation which appears in atmospheric science, and Burgers equation which is perhaps the simplest active scalar. Many questions about regularity and properties of solutions of these equations remain open. I will talk about the recently introduced idea of nonlocal maximum principle and progress it led to. I will also discuss some questions that remain open, and how these questions relate to other problems of interest in mathematical fluid mechanics.