Volume 7, Issue 2, May 2000, Pages 136 - 169
Existence and Homogenization of the Rayleigh-Bénard Problem
- Björn BIRNIR, Nils SVANSTEDT
- Corresponding Author
- Björn BIRNIR
Available Online 13 December 2006.
- https://doi.org/10.2991/jnmp.2000.7.2.6How to use a DOI?
- 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.
Cite this article
TY - JOUR AU - Björn BIRNIR AU - Nils SVANSTEDT PY - 2006 DA - 2006/12 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 - BIRNIR2006 ER -