Two-dimensional pseudo-steady supersonic flow around a sharp corner

In this paper, we study the expansion problem which arises in a two-dimensional (2D) isentropic pseudo-steady supersonic flow expanding into vacuum around a sharp corner. The problem catches interaction of an incomplete centered simple wave with a backward planar rarefaction wave as well as interaction of a simple wave with rigid wall boundary of the 2D self-similar Euler equations. Using the methods of characteristic decompositions and invariant regions, we mainly deal with the interaction of two symmetric non-planar simple waves of the 2D self-similar Euler equations to obtain the global existence of the solution for the interaction of the simple wave with rigid wall boundary. It follows the global existence of the solution up to the interface of supersonic flow with vacuum of the expansion problem.