Steve Shkoller, UC Davis
Abstract: Free-boundary problems in fluid dynamics involve solutions to Euler equations on domains which are evolving in time and which are a priori unknown. The boundaries of these fluid domains have evolution laws which require knowledge of the fluid flow, while solving for the fluid flow, in turn, requires information about the geometry of the boundary. Such moving boundaries arise in the study of ocean waves, shock waves, phase transitions, and many other interesting wave patterns. In this lecture, I will survey some of the recent results in this area.