Interaction of a centered simple wave and a planar rarefaction wave of the two-dimensional Euler equations for pseudo-steady compressible flow

Abstract

In this paper, we study the expansion problem which arises as two-dimensional (2D) pseudo-steady supersonic flow turns a sharp corner and expands into vacuum. The problem catches interaction of a centered simple wave and a backward planar rarefaction wave, which is deduced a Goursat problem for 2D self-similar Euler equations for compressible flow. By the methods of characteristic decomposition and invariant regions, we get the hyperbolicity in the wave interaction domain and prior C1 estimates of solutions to the Goursat problem. The global solution up to the interface of gas with vacuum to the expansion problem is obtained constructively.