Shock Reflection and Free Boundary Problems

In this talk we describe some recent work on shock

reflection problems for the potential flow equation. We will

start with discussion of shock reflection phenomena. Then we

will describe the results on existence, structure and

regularity of global solutions to regular shock reflection. The

approach is to reduce the shock reflection problem to a free

boundary problem for a nonlinear elliptic equation, with

ellipticity degenerate near a part of the boundary (the sonic

arc). We will discuss techniques to handle such free boundary

problems and degenerate elliptic equations. This talk is based

on joint works with Gui-Qiang Chen, and with Myoungjean Ba