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Asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh‐Bénard convection at large Prandtl number

We study asymptotic behavior of the global attractors to the Boussinesq system for Rayleigh‐Bénard convection at large Prandtl number. In particular, we show that the global attractors to the Boussinesq system for Rayleigh‐Bénard convection converge to that of the infinite‐Prandtl‐number model for convection as the Prandtl number approaches infinity. This offers partial justification of the infinite‐Prandtl‐number model for convection as a valid simplified model for convection at large Prandtl number even in the long‐time regime. © 2006 Wiley Periodicals, Inc.