Skip to main content
Article thumbnail
Location of Repository

EXISTENCE THEORY AND STRONG ATTRACTORS FOR THE RAYLEIGH-BÉNARD PROBLEM WITH A LARGE ASPECT RATIO

By Björn Birnir and Nils Svanstedt

Abstract

Abstract. The Navier-Stokes equation driven by heat conduction is studied. It is proven that if the driving force is small then the solutions of the Navier-Stokes equation are ultimately regular. 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 numer close to one, we prove the ultimate existence and regularity of a global strong solution to the 3D Navier-Stokes equation coupled with a heat equation, and the existence of a maximal B-attractor. Examples of simple B-attractors from pattern formation are given and a method to study their instabilities proposed. 1. Introduction. I

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.352.7515
Provided by: CiteSeerX
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://citeseerx.ist.psu.edu/v... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.