Journal of Nonlinear Mathematical Physics

Volume 7, Issue 2, May 2000, Pages 136 - 169

Existence and Homogenization of the Rayleigh-Bénard Problem

Authors
Björn BIRNIR, Nils SVANSTEDT
Corresponding Author
Björn BIRNIR
Available Online 1 May 2000.
DOI
https://doi.org/10.2991/jnmp.2000.7.2.6How to use a DOI?
Abstract
The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-Bénard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-Bénard experiments with Prandtl number close to one, we prove the existence of a global strong solution to the 3D Navier-Stokes equation coupled with a heat equation, and the existence of a maximal B-attractor. A rigorous two-scale limit is obtained by homogenization theory. The mean velocity field is obtained by averaging the two-scale limit over the unit torus in the local variable.
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
7 - 2
Pages
136 - 169
Publication Date
2000/05
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2000.7.2.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Björn BIRNIR
AU  - Nils SVANSTEDT
PY  - 2000
DA  - 2000/05
TI  - Existence and Homogenization of the Rayleigh-Bénard Problem
JO  - Journal of Nonlinear Mathematical Physics
SP  - 136
EP  - 169
VL  - 7
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2000.7.2.6
DO  - https://doi.org/10.2991/jnmp.2000.7.2.6
ID  - BIRNIR2000
ER  -