Asymptotic analysis of compressible, viscous, and heat conducting fluids

0444396 - MÚ 2016 RIV JP eng C - Conference Paper (international conference)
Feireisl, Eduard
Asymptotic analysis of compressible, viscous, and heat conducting fluids.
Nonlinear Dynamics in Partial Differential Equations. Tokyo: Mathematical Society of Japan, 2015 - (Ei, S.; Kawashima, S.; Kimura, M.; Mizumachi, T.), s. 1-33. Advanced Studies in Pure Mathematics, 64. ISBN 978-4-86497-022-8.
[4th MSJ-SI International Conference Nonlinear Dynamics in Partial Differential Equations. Kyushu (JP), 12.09.2011-21.09.2011]
R&D Projects: GA ČR GA201/09/0917
Institutional support: RVO:67985840
Keywords : Navier-Stokes-Fourier system * long-time behavior * scale analysis
Subject RIV: BA - General Mathematics

This is a survey of recent results concerning the mathematical theory of compressible, viscous, and heat conducting fluids. Starting from the basic physical principles, notably the First and Second laws of thermodynamics, we introduce a concept of weak solutions to complete fluid systems and analyze their asymptotic behavior. In particular, the long time behavior and scale analysis will be performed. We also introduce a new concept of relative entropy for the system and show how it can be used in the problem of weak-strong uniqueness and the inviscid limits.
Permanent Link: http://hdl.handle.net/11104/0246940