Shock Reflection, von Neumann conjectures, and free boundary problems

We discuss shock reflection problem for compressible gas dynamics, various patterns of reflected shocks, and von Neumann conjectures on transition between regular and Mach reflections. Then

we will talk about recent results on existence of regular reflection solutions for potential flow equation up to the detachment angle, and discuss some techniques. The approach is to reduce the shock

reflection problem to a free boundary problem for a nonlinear equation of mixed elliptic-hyperbolic type. Open problems will also be discussed. The talk is based on the joint work with Gui-Qiang Chen.