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Free boundary problems in shock reflection/diffraction and related transonic flow problems. (English) Zbl 1353.76045

Summary: Shock waves are steep wavefronts that are fundamental in nature, especially in high-speed fluid flows. When a shock hits an obstacle, or a flying body meets a shock, shock reflection/diffraction phenomena occur. In this paper, we show how several long-standing shock reflection/diffraction problems can be formulated as free boundary problems, discuss some recent progress in developing mathematical ideas, approaches and techniques for solving these problems, and present some further open problems in this direction. In particular, these shock problems include von Neumann’s problem for shock reflection-diffraction by two-dimensional wedges with concave corner, Lighthill’s problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer’s problem for supersonic flow impinging onto solid wedges, which are also fundamental in the mathematical theory of multidimensional conservation laws.

MSC:

76H05 Transonic flows
76L05 Shock waves and blast waves in fluid mechanics
35R35 Free boundary problems for PDEs
35Q35 PDEs in connection with fluid mechanics
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