Existence and Homogenization of the Rayleigh-Bénard Problem
作者:
Björn Birnir,
Nils Svanstedt,
期刊:
Journal of Nonlinear Mathematical Physics
(Taylor Available online 2000)
卷期:
Volume 7,
issue 2
页码: 136-169
ISSN:1402-9251
年代: 2000
DOI:10.2991/jnmp.2000.7.2.3
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
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.
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