On the energy dissipation rate of solutions to the compressible isentropic Euler system

2013/12/17 by Elisabetta Chiodaroli, Ondřej Kreml · 2 citations
Mathematics · #math.AP

paper · pdf · doi:10.1007/s00205-014-0771-8

arxiv created 2013/12/17 · arxiv updated 2014/08/26

Abstract

In this paper we extend and complement some recent results by Chiodaroli, De Lellis and Kreml on the well-posedness issue for weak solutions of the compressible isentropic Euler system in 2 space dimensions with pressure law p(ρ)=ρ^γ, γ≥ 1. First we show that every Riemann problem whose one-dimensional self-similar solution consists of two shocks admits also infinitely many two-dimensional admissible bounded weak solutions (not containing vacuum) generated by the method of De Lellis and Székelyhidi. Moreover we prove that for some of these Riemann problems and for 1≤ γ< 3 such solutions have greater energy dissipation rate than the self-similar solution emanating from the same Riemann data. We therefore show that the maximal dissipation criterion proposed by Dafermos does not favour the classical self-similar solutions.

Cited by

• An overview of some recent results on the Euler system of isentropic gas\n dynamics
• Selection criteria for the compressible Euler equations: numerical study

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