Long time behavior and attractors for energetically insulated fluid systems
type: Item
instance of: scholarly article
title: Long time behavior and attractors for energetically insulated fluid systems
zbMATH Open document ID: 1203.35188
author: Eduard Feireisl
published in: Discrete and Continuous Dynamical Systems
publication date: 2010-06-23T00:00:00Z
review text: The author continues previous work on the fluid problems and specifically the Navier-Stokes-Fourier system [\textit{E. Feireisl} and \textit{A. Novotný}, Singular limits in thermodynamics of viscous fluids. Advances in Mathematical Fluid Mechanics. Basel: Birkhäuser (2009; Zbl 1176.35126); \textit{E. Feireisl} and \textit{H. Petzeltová}, J. Dyn. Differ. Equations 19, No. 3, 685--707 (2007; Zbl 1168.35032); \textit{E. Feireisl}, Comput. Math. Appl. 53, No. 3--4, 461--490 (2007; Zbl 1122.76075)]. This system consists of the conservation law of mass, the balance of momentum, an entropy production equation and Fourier's law. It is consistent with the second law of thermodynamics and the author emposes insulating boundary conditions for the energy flux. As a first result, the static states are shown to consist of a two-parameter family and to maximize total entropy among all states with the same mass and total energy. The main result is that (for the weak formulation of the Navier-Stokes-Fourier system) the distance of trajectories to the set of static solutions tends to zero \textit{uniformly}. The author concludes with a number of remarks on modifications and extensions, for instance that non-insulating boundary conditions can have a dramatic effect on the long term dynamics.
Mathematics Subject Classification ID: 35Q30
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 37N10
Mathematics Subject Classification ID: 76F02
Mathematics Subject Classification ID: 80A17
zbMATH DE Number: 5725449
zbMATH Keywords: Navier-Stokes-Fourier system
zbMATH Keywords: attractor
zbMATH Keywords: long time behavior
zbMATH Keywords: rational thermodynamics
reviewed by: Jens D. M. Rademacher
MaRDI profile type: Publication
full work available at URL: dcds.2010.27.1587
OpenAlex ID: W1997741522
Wikidata QID: Q59316550
DOI: 10.3934/DCDS.2010.27.1587
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description: scientific article; zbMATH DE number 5725449