Shocks make the Riemann problem for the full Euler system in multiple space dimensions ill-posed

Abstract

The question of (non-)uniqueness of one-dimensional self-similar solutions to the Riemann problem for hyperbolic systems of gas dynamics in the class of multi-dimensional admissible weak solutions was addressed in recent years in several papers culminating in [] with the proof that the Riemann problem for the isentropic Euler system with a power law pressure is ill-posed if the one-dimensional self-similar solution contains a shock. Then the natural question arises whether the same holds also for a more involved system of equations, the full Euler system. After the first step in this direction was made in [], where ill-posedness was proved in the case of two shocks appearing in the self-similar solution, we prove in this paper that the presence of just one shock in the self-similar solution implies the same outcome, i.e. the existence of infinitely many admissible weak solutions to the multi-dimensional problem.