Advanced Studies in Pure Mathematics

Asymptotic analysis of compressible, viscous and heat conducting fluids

Eduard Feireisl

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

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

Permanent link to this document euclid.aspm/1540934201

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

Export citation