Nonlocal maximum principles for active scalars

PDE Seminar
Tuesday, October 23, 2012 - 3:05pm
1 hour (actually 50 minutes)
Skiles 006
Department of Mathematics, University of Wisconsin, Madison
Active scalars appear in many problems of fluid dynamics. The most common examples of active scalar equations are 2D Euler, Burgers, and 2D surface quasi-geostrophic (SQG) equations. Many questions about regularity and properties of solutions of these equations remain open. I will discuss the recently introduced idea of nonlocal maximum principle, which helped prove global regularity of solutions to the critical SQG equation. I will describe some further recent developments on regularity and blowup of solutions to active scalar equations.