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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Alexander Kiselev
Afilliation: University of Wisconsin, Madison

Title: Nonlocal Maximum Principles for Active Scalars

Abstract: Active scalar equations appear in many instances in fluid mechanics. Examples include 2D Euler, Burgers, and surface quasi-geostrophic (SQG) equations. In the past few years, several new approaches have been developed to study the properties of solutions in critical and supercritical regime.

I will review the techniques based on control of moduli of continuity of the solutions. I will then talk about recent results in the supercritical regime, including finite time regularization of solutions for SQG and Burgers, and global regularity for slightly supercritical SQG equation.

Slides: KiselevSasha.pdf