Shock Reflection and Free Boundary Problems

When a plane shock hits a wedge head on, it experiences a reflection and then a self-similar reflected shock moves outward as the original shock moves forward in time. Experimental, computational, and asymptotic analysis has shown that various patterns of reflected shocks may occur, including regular and Mach reflection. However, most fundamental issues for shock reflection have not been understood, including the transition among the different patterns of shock reflection, and there has been no rigorous mathematical result on the global existence and structural stability of shock reflection, especially for potential flow which has widely been used in aerodynamics. In the recent joint work with G.-Q. Chen, we establish the global existence and stability of solutions to shock reflection by a large-angle wedge for potential flow. In the talk I will describe the result and outline the techniques used in the work.

Mikhail Feldman, University of Wisconsin, Madison

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