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Infinite Prandtl number limit of Rayleigh-Bénard convection. (English) Zbl 1112.76032
Taking into account the effect of rotation, the author rigorously justifies on a finite time interval the infinite Prandtl number model of convection as the Prandtl number approaches infinity in the Boussinesq approximation to Rayleigh-Bénard convection. The proof is based on a two-time-scale approximation which allows to decompose the effective dynamics of the Boussinesq system into the infinite Prandtl number dynamics plus initial layer plus lower-order terms. It is argued that the developed method is applicable to other singular limit problems.

MSC:
76E06 Convection in hydrodynamic stability
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76R05 Forced convection
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