naa a22 4500 510760872 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s13163-013-0126-2 doi (NATIONALLICENCE)springer-10.1007/s13163-013-0126-2 Feireisl Eduard Faculty of Mathematics and Physics, Mathematical Institute, Charles University in Prague, Sokolovská 83, 186 75, Prague 8, Czech Republic aut Mathematical analysis of fluids in motion: from well-posedness to model reduction [Elektronische Daten] [Eduard Feireisl] 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. Universidad Complutense de Madrid, 2013 Navier-Stokes-Fourier system nationallicence Compressible fluid nationallicence Singular limits nationallicence Relative entropy nationallicence Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 299-340 1139-1138 26:2<299 2013 26 13163 https://doi.org/10.1007/s13163-013-0126-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-013-0126-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Feireisl Eduard Faculty of Mathematics and Physics, Mathematical Institute, Charles University in Prague, Sokolovská 83, 186 75, Prague 8, Czech Republic aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/2(2013-07-01), 299-340 1139-1138 26:2<299 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer