Nonlocal maximum principles for active scalars

Series: 
PDE Seminar
Tuesday, October 23, 2012 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Department of Mathematics, University of Wisconsin, Madison
Organizer: 
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.