Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

Details Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System Shock Diffraction by Convex Cornered Wedges for the Nonlinear Wave System

2012-02-04

arxiv.org/abs/1202.0856v1

Mathematics

Analysis of PDEs

75 pages;7 figures

Scientific paper

We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a boundary value problem for second-order nonlinear partial differential equations of mixed elliptic-hyperbolic type in an unbounded domain. It can be further reformulated as a free boundary problem for nonlinear degenerate elliptic equations of second order. We establish a first global theory of existence and regularity for this shock diffraction problem. In particular, we establish that the optimal regularity for the solution is $C^{0,1}$ across the degenerate sonic boundary. To achieve this, we develop several mathematical ideas and techniques, which are also useful for other related problems involving similar analytical difficulties.

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