Mathematical theory of viscous fluids: Retrospective and      future perspectives

Eduard Feireisl

doi:10.3934/dcds.2010.27.533

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2010, Volume 27, Issue 2: 533-555. Doi: 10.3934/dcds.2010.27.533

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Mathematical theory of viscous fluids: Retrospective and future perspectives

Eduard Feireisl^1,

1.
Mathematical Institute AV ČR, Žitná 25, 115 67 Praha 1

Received: October 2009

Revised: February 2010

Published: July 2010

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Abstract

We review the recent state of art of the mathematical theory of viscous, compressible, and heat conducting fluids. We emphasize the significant role of the Second law of thermodynamics in our approach. Qualitative properties of solutions and relations between different models are also discussed.

Keywords:

Navier-Stokes-Fourier system,
global existence,
qualitative properties of compressible fluids.

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

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