Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

Abstract

We study the Riemann problem for the multidimensional compressible isentropic Euler equations. Using the framework developed by Chiodaroli, De Lellis, Kreml and based on the techniques of De Lellis and Székelyhidi, we extend our previous results and prove that whenever the initial Riemann data give rise to a self-similar solution consisting of one admissible shock and one rarefaction wave and are not too far from lying on a simple shock wave, the problem admits also infinitely many admissible weak solutions.

20 pages, 10 figures

References in corpus (1)

• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock

Cited by in corpus (11)

• The Riemann problem for the multidimensional isentropic system of gas dynamics is ill-posed if it contains a shock
• Vanishing viscosity limit to the planar rarefaction wave for the two-dimensional compressible Navier-Stokes equations
• Kolmogorov-Type Theory of Compressible Turbulence and Inviscid Limit of the Navier-Stokes Equations in ${\mathbb{R}}^3$
• Non-uniqueness of admissible weak solution to the Riemann problem for the full Euler system in 2D
• Shocks Make the Riemann Problem for the Full Euler System in Multiple Space Dimensions Ill-posed
• Global ill-posedness for a dense set of initial data to the Isentropic system of gas dynamics
• A New Convex Integration Approach for the Compressible Euler Equations and Failure of the Local Maximal Dissipation Criterion
• On contact discontinuities in multi-dimensional isentropic Euler equations
• Contact discontinuities for 2-D isentropic Euler are unique in 1-D but wildly non-unique otherwise
• The Rayleigh-Taylor instability with local energy dissipation
• Stability of the planar rarefaction wave to two-dimensional compressible Navier-Stokes equations