JournalsaihpcVol. 32, No. 1pp. 225–243

On the weak solutions to the equations of a compressible heat conducting gas

  • Elisabetta Chiodaroli

    Mathematisches Institut, Universität Leipzig, Augustusplatz 10, D-04009 Leipzig, Germany

  • Eduard Feireisl

    Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic

  • Ondřej Kreml

    Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland
On the weak solutions to the equations of a compressible heat conducting gas cover
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Abstract

We consider the weak solutions to the Euler–Fourier system describing the motion of a compressible heat conducting gas. Employing the method of convex integration, we show that the problem admits infinitely many global-in-time weak solutions for any choice of smooth initial data. We also show that for any initial distribution of the density and temperature, there exists an initial velocity such that the associated initial-value problem possesses infinitely many solutions that conserve the total energy.

Cite this article

Elisabetta Chiodaroli, Eduard Feireisl, Ondřej Kreml, On the weak solutions to the equations of a compressible heat conducting gas. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 1, pp. 225–243

DOI 10.1016/J.ANIHPC.2013.11.005