Publication at Faculty of Mathematics and Physics |
2013
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.