Free-boundary problems in fluid dynamics
Steve Shkoller (University of California at Davis)

I will discuss a priori estimates, existence theorems, and the splash singularity for the incompressible and compressible Euler equations with moving free-boundary (and vacuum). I also explain how methods developed for the Euler equations provide a natural framework for the analysis of the classical Stefan problem. Finally, I will explain a new strategy for the analysis of the compressible MHD equations.