Existence of solutions to gas expansion problem through a sharp corner for 2‐D Euler equations with general equation of state

Abstract

In this article, we study the gas expansion problem by turning a sharp corner into a vacuum for the two‐dimensional (2‐D) pseudosteady compressible Euler equations with a convex equation of state. This problem can be considered as the interaction of a centered simple wave with a planar rarefaction wave. To obtain the global existence of a solution up to the vacuum boundary of the corresponding 2‐D Riemann problem, we consider several Goursat‐type boundary value problems for 2‐D self‐similar Euler equations and use the ideas of characteristic decomposition and bootstrap method. Further, we formulate 2‐D‐modified shallow water equations newly and solve a dam‐break‐type problem for them as an application of this work. Moreover, we also recover the results from the available literature for certain equations of states that provide a check that the results obtained in this article are actually correct.