Volume 7, Issue 2, May 2000, Pages 136 - 169
Existence and Homogenization of the Rayleigh-Bénard Problem
Björn Birnir, Nils Svanstedt
Received 23 June 1999, Revised 11 December 1999, Accepted 17 December 1999, Available Online 1 May 2000.
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- 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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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 -