Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 1 - 33
Asymptotic analysis of compressible, viscous and heat conducting fluids
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.
Received: 18 April 2012
Revised: 7 December 2012
First available in Project Euclid: 30 October 2018
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Feireisl, Eduard. Asymptotic analysis of compressible, viscous and heat conducting fluids. Nonlinear Dynamics in Partial Differential Equations, 1--33, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410001. https://projecteuclid.org/euclid.aspm/1540934201