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

Abstract

The problem of the two-dimensional pseudo-steady supersonic isothermal flow around a sharp corner expanding into vacuum is studied in this article. It is worth noting that the gas will diffuse to infinity, that is, there is no vacuum boundary in this work. The essence of this problem is the interaction of the centered simple wave with the planar rarefaction wave, which can be solved by the Goursat problem for the two-dimensional self-similar Euler equations. Through the methods of characteristic decompositions and invariant regions, we establish a priori C1 estimates and the hyperbolicity of the solution in the wave interaction domain. The global existence of solution to the gas expansion problem is obtained constructively.