Relative entropies in thermodynamics of complete fluid systems

Eduard Feireisl

doi:10.3934/dcds.2012.32.3059

Article Contents

2012, Volume 32, Issue 9: 3059-3080. Doi: 10.3934/dcds.2012.32.3059

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Relative entropies in thermodynamics of complete fluid systems

Eduard Feireisl^1,

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

Received: October 31, 2011

Revised: February 29, 2012

Published: August 2012

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Abstract

We introduce the notion of relative entropy in the framework of thermodynamics of compressible, viscous and heat conducting fluids. The relative entropy is constructed on the basis of a thermodynamic potential called ballistic free energy and provides stability of solutions to the associated Navier-Stokes-Fourier system with respect to perturbations. The theory is illustrated by applications to problems related to the long time behavior of solutions and the problem of weak-strong uniqueness.

Keywords:

Navier-Stokes-Fourier system,
relative entropy,
qualitative properties of compressible fluids.

Mathematics Subject Classification: Primary: 35Q30; Secondary: 35B25.

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