Stability of the Isentropic Riemann Solutions of the Full Multidimensional Euler System

Abstract

We consider the complete Euler system describing the time evolution of an inviscid nonisothermal gas. We show that the rarefaction wave solutions of the one-dimensional (1-D) Riemann problem are stable, in particular unique, in the class of all bounded weak solutions to the associated multidimensional problem. This may be seen as a counterpart of the nonuniqueness results of physically admissible solutions emanating from 1-D shock waves constructed recently by the method of convex integration.