Free Boundary Problems in Shock Reflection/Diffraction and Related Transonic Flow Problems

摘要

Shock waves are steep wave fronts that are fundamental in nature, especiallyin high-speed fluid flows. When a shock hits an obstacle, or a flying bodymeets a shock, shock reflection/diffraction phenomena occur. In this paper, weshow how several longstanding shock reflection/diffraction problems can beformulated as free boundary problems, discuss some recent progress indeveloping mathematical ideas, approaches, and techniques for solving theseproblems, and present some further open problems in this direction. Inparticular, these shock problems include von Neumann's problem for shockreflection-diffraction by two-dimensional wedges with concave corner,Lighthill's problem for shock diffraction by two-dimensional wedges with convexcorner, and Prandtl-Meyer's problem for supersonic flow impinging onto solidwedges, which are also fundamental in the mathematical theory ofmultidimensional conservation laws.