Non-uniqueness of admissible weak solution to the Riemann problem for the full Euler system in 2D

Abstract

The question of well- and ill-posedness of entropy admissible solutions to the multi-dimensional systems of conservation laws has been studied recently in the case of isentropic Euler equations. In this context special initial data were considered, namely the 1D Riemann problem which is extended trivially to a second space dimension. It was shown that there exist infinitely many bounded entropy admissible weak solutions to such a 2D Riemann problem for isentropic Euler equations, if the initial data give rise to a 1D self-similar solution containing a shock. In this work we study such a 2D Riemann problem for the full Euler system in two space dimensions and prove the existence of infinitely many bounded entropy admissible weak solutions in the case that the Riemann initial data give rise to the 1D self-similar solution consisting of two shocks and possibly a contact discontinuity.

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Cited by in corpus (6)

• Shocks Make the Riemann Problem for the Full Euler System in Multiple Space Dimensions Ill-posed
• Uniqueness of a planar contact discontinuity for 3D compressible Euler system in a class of zero dissipation limits from Navier-Stokes-Fourier system
• Global ill-posedness for a dense set of initial data to the Isentropic system of gas dynamics
• On the density of wild initial data for the compressible Euler system
• Finite time stability for the Riemann problem with extremal shocks for a large class of hyperbolic systems
• Further studies on numerical instabilities of Godunov-type schemes for strong shocks