Some existence results for the Navier-Stokes equation driven by heat conduction

• Main Authors: Bjorn Birnir, Nils Svanstedt
• Other Authors: The Pennsylvania State University CiteSeerX Archives
• Format: Text
• Language: English
• Subjects: Chalmers; Iceland
• Online Access: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.240; http://www.math.ucsb.edu/~birnir/papers/rb.ps

The Navier-Stokes equation driven by heat conduction is studied. As a prototype we consider Rayleigh-B'enard convection, in the Boussinesq approximation. Under a large aspect ratio assumption, which is the case in Rayleigh-B'enard experiments with Prandtl numer 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. PACS numbers, 44.25.+f, 47.27.Te and The University of Iceland, Science Institute, Dunhaga, Reykjav'ik 107, Iceland. y Email: [e-mail] and URL: www.math.ucsb.edu/~birnir z and Department of Mathematics, Chalmers University of Technology and Goteborg University S-412 96 Goteborg, Sweden. x Email: [e-mail] 1 Introduction In this paper we study the Navier-Stokes equation driven by heat conduction. Under a large aspect ratio assumption (the spatial domain being a thin layer) we prove the existence of a global strong solution. T.