Existence and dimension of the attractor for the Bénard problem on channel-like domains.
type: Item
instance of: scholarly article
title: Existence and dimension of the attractor for the Bénard problem on channel-like domains.
zbMATH Open document ID: 1049.37046
author: Marco Cabral
author: Ricardo M. S. Rosa
author: R. Temam
published in: Discrete and Continuous Dynamical Systems
publication date: 2004-07-01T00:00:00Z
review text: The Bénard system is a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the temperature. The velocity influences the diffusion of the temperature and the temperature induces a convective motion of the fluid via the Boussinesq approximation. For this problem, the authors prove the existence of global solutions and of the global attractor in the usual \(L^2\)-like space. Also, it is proved that the global attractor has finite Hausdorff and fractal dimensions, which are estimated in terms of suitable Reynolds, Prandtl, Grashof and Rayleigh numbers. The used approach, unlike the previous works, avoids the use of the maximum principle which would be problematic in this context.
Mathematics Subject Classification ID: 37L30
Mathematics Subject Classification ID: 35B41
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 76E06
Mathematics Subject Classification ID: 76D03
zbMATH DE Number: 2077709
zbMATH Keywords: Bénard problem
zbMATH Keywords: noncompact systems
zbMATH Keywords: global attractor
zbMATH Keywords: fractal dimension
reviewed by: Boris V. Loginov
MaRDI profile type: Publication
full work available at URL: dcds.2004.10.89
OpenAlex ID: W2042810041
DOI: 10.3934/DCDS.2004.10.89
description: scientific article; zbMATH DE number 2077709