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An overview of some recent results on the Euler system of isentropic gas dynamics

  • Elisabetta Chiodaroli
  • Ondřej Kreml
Article
  • 74 Downloads

Abstract

This overview is concerned with the well-posedness problem for the isentropic compressible Euler equations of gas dynamics. The results we present are in line with the programof investigatingthe efficiency of different selection criteria proposed in the literature in order to weed out non-physical solutions to more-dimensional systems of conservation laws and they build upon the method of convex integration developed by De Lellis and Székelyhidi for the incompressible Euler equations. Mainly following [5], we investigate the role of the maximal dissipation criterion proposed by Dafermos in [6]: we prove how, for specific pressure laws, some non-standard (i.e. constructed via convex integration methods) solutions to the Riemann problem for the isentropic Euler system in two space dimensions have greater energy dissipation rate than the classical self-similar solution emanating from the same Riemann data. We therefore show that the maximal dissipation criterion proposed by Dafermos does not favour in general the self-similar solutions.

Keywords

hyperbolic systems of conservation laws Riemann problem admissible solutions entropy rate criterion ill-posedness convex integration 

Mathematical subject classification

Primary: 35L65 Secondary: 35L67, 35L45 

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Copyright information

© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  1. 1.EPFL LausanneLausanneSwitzerland
  2. 2.Institute of MathematicsAcademy of Sciences of the Czech RepublicPraha 1Czech Republic

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