Nonlocal Maximum Principles for Active Scalars

A. Kiselev, University of Wisconsin
Fine Hall 314

Active scalar equations play an important role in modeling fluids. Some of the best known examples of active scalars are the 2D Euler equation, the surface quasi-geostrophic (SQG) equation, and the Burgers equation. Most active scalars are nonlocal, making detailed analysis of their solutions challenging. I will review recent progress in this area. In particular, I will talk about a new recently developed method for analysis of active scalars, and its applications to studies of the regularity properties of solutions.