# American Institute of Mathematical Sciences

May  2010, 27(2): 533-555. doi: 10.3934/dcds.2010.27.533

## Mathematical theory of viscous fluids: Retrospective and future perspectives

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

Received  October 2009 Revised  February 2010 Published  February 2010

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.
Citation: Eduard Feireisl. Mathematical theory of viscous fluids: Retrospective and future perspectives. Discrete and Continuous Dynamical Systems, 2010, 27 (2) : 533-555. doi: 10.3934/dcds.2010.27.533
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