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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids pp 1–27Cite as

Concepts of Solutions in the Thermodynamics of Compressible Fluids

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Abstract

The objective of this chapter is to highlight the recent development of the mathematical theory of complete fluids. The word complete means the governing system of equations is rich enough to incorporate the basic physical principles, in particular the first, second, and third laws of thermodynamics, in a correct and integral way into the mathematical model. In the whole text, the platform of classical continuum mechanics is adopted, where the fluid motion is described in terms of observable macroscopic quantities: the mass density, the (absolute) temperature, and the (bulk) velocity.

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Acknowledgements

The research of E.F. leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ ERC Grant Agreement 320078. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.

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Authors and Affiliations

  1. Evolution Differential Equations (EDE), Academy of Sciences of the Czech Republic, Institute of Mathematics, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

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  1. Eduard Feireisl
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Correspondence to Eduard Feireisl .

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Editors and Affiliations

  1. Tokyo, Tokyo, Japan

    Yoshikazu Giga

  2. Toulon, Var, France

    Antonin Novotny

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Feireisl, E. (2016). Concepts of Solutions in the Thermodynamics of Compressible Fluids. In: Giga, Y., Novotny, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-10151-4_31-1

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  • DOI: https://doi.org/10.1007/978-3-319-10151-4_31-1

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  • Online ISBN: 978-3-319-10151-4

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