Calculus of Variations and Geometric Measure Theory

E. Chiodaroli - E. Feireisl - O. Kreml

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

created by chiodaroli on 02 Jul 2013
modified on 20 Apr 2015


Published Paper

Inserted: 2 jul 2013
Last Updated: 20 apr 2015

Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis
Volume: 32
Number: 1
Pages: 225–243
Year: 2015
Doi: doi:10.1016/j.anihpc.2013.11.005
Links: PDF


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.