The 2-d isentropic compressible Euler equations may have infinitely many solutions which conserve energy

Abstract

We consider the 2-d isentropic compressible Euler equations. It was shown in by E. Chiodaroli, C. De Lellis and O. Kreml that there exist Riemann initial data as well as Lipschitz initial data for which there exist infinitely many weak solutions that fulfill an energy inequality. In this note we will prove that there is Riemann initial data for which there exist infinitely many weak solutions that conserve energy, i.e. they fulfill an energy equality. As in the aforementioned paper we will also show that there even exists Lipschitz initial data with the same property.

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 (7)

• On oscillatory solutions to the complete Euler system
• 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
• Prandtl-Meyer Reflection Configurations, Transonic Shocks, and Free Boundary Problems
• A New Convex Integration Approach for the Compressible Euler Equations and Failure of the Local Maximal Dissipation Criterion
• Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential Flow
• The Rayleigh-Taylor instability with local energy dissipation