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Mathematical analysis of fluids in motion: from well-posedness to model reduction

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Abstract

This paper reviews some recent results on the Navier-Stokes-Fourier system governing the evolution of a general compressible, viscous, and heat conducting fluid. We discuss several concepts of weak solutions, in particular, using the implications of the Second law of thermodynamics. We introduce the concept of relative entropy and dissipative solution and show the principle of weak-strong uniqueness. The second part of the paper is devoted to problems of model reduction and the related singular limits. Several examples of singular limits are presented: The incompressible limit, the inviscid limit, the low Rossby number limit and their combinations.

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Acknowledgments

Eduard Feireisl acknowledges the support of the project LL1202 in the programme ERC-CZ funded by the Ministry of Education, Youth and Sports of the Czech Republic.

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

    Eduard Feireisl

  2. Faculty of Mathematics and Physics, Mathematical Institute, Charles University in Prague, Sokolovská 83, 186 75 , Prague 8, Czech Republic

    Eduard Feireisl

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Feireisl, E. Mathematical analysis of fluids in motion: from well-posedness to model reduction. Rev Mat Complut 26, 299–340 (2013). https://doi.org/10.1007/s13163-013-0126-2

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