# American Institute of Mathematical Sciences

September  2012, 32(9): 3059-3080. doi: 10.3934/dcds.2012.32.3059

## Relative entropies in thermodynamics of complete fluid systems

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

Received  November 2011 Revised  March 2012 Published  April 2012

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.
Citation: Eduard Feireisl. Relative entropies in thermodynamics of complete fluid systems. Discrete & Continuous Dynamical Systems - A, 2012, 32 (9) : 3059-3080. doi: 10.3934/dcds.2012.32.3059
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##### References:
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