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Shock reflection, free boundary problems and degenerate elliptic equationsPDE and Applied Math Seminar
We discuss shock reflection problem for compressible gas dynamics, 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 regularity of solutions, and geometric properties of the shock curve. Our 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, including uniqueness.
The talk is based on the joint works with Gui-Qiang Chen, as well as with Myoungjean Bae and Wei Xiang.