Advanced Studies in Pure Mathematics

Asymptotic analysis of compressible, viscous and heat conducting fluids

Eduard Feireisl

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Abstract

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.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 1-33

Dates
Received: 18 April 2012
Revised: 7 December 2012
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934201

Digital Object Identifier
doi:10.2969/aspm/06410001

Mathematical Reviews number (MathSciNet)
MR3381190

Zentralblatt MATH identifier
1335.35181

Subjects
Primary: 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 35Q35: PDEs in connection with fluid mechanics 35E15: Initial value problems

Keywords
Navier–Stokes–Fourier system long-time behavior scale analysis

Citation

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


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