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The perturbed problem on the Boussinesq system of Rayleigh-Bénard convection. (English) Zbl 1300.35103

Summary: In this paper, the infinite Prandtl number limit of Rayleigh-Bénard convection is studied. For well prepared initial data, the convergence of solutions in \(L^\infty(0,t;H^2(G))\) is rigorously justified by analysis of asymptotic expansions.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
35C20 Asymptotic expansions of solutions to PDEs
35K57 Reaction-diffusion equations
76R05 Forced convection
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