Concepts of Solutions in the Thermodynamics of Compressible Fluids

  • Eduard FeireislEmail author
Living reference work entry


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.


Weak Solution Euler System Total Energy Balance Dissipative Solution Internal Energy Balance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Evolution Differential Equations (EDE), Academy of Sciences of the Czech Republic, Institute of MathematicsPraha 1Czech Republic

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