Georgia Institute of Technology School of Mathematics | Georgia Institute of Technology | Atlanta, GA

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.