Nonlocal maximum principles for active scalars
- Series
- PDE Seminar
- Time
- Tuesday, October 23, 2012 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Alexander Kiselev – 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.