Some existence results for the Navier-Stokes equation driven by heat conduction
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 e...
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| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.240 http://www.math.ucsb.edu/~birnir/papers/rb.ps |
| Summary: | 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: birnir@math.ucsb.edu 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: nilss@math.chalmers.se 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. |
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