Stability of the isentropic Riemann solutions of the full multidimensional Euler system

TL;DR

This paper proves the stability and uniqueness of rarefaction wave solutions in the multidimensional Euler system, contrasting recent non-uniqueness results for shock waves, thus advancing understanding of solution behavior in inviscid gas dynamics.

Contribution

It demonstrates the stability and uniqueness of 1D rarefaction wave solutions within the multidimensional Euler system, providing new insights into solution stability.

Findings

Rarefaction waves are stable in multidimensional Euler flows.

Unique solutions exist for the class of bounded weak solutions.

Contrasts with non-uniqueness results for shock waves.

Abstract

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