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The inviscid limit behavior for smooth solutions of the Boussinesq system. (English) Zbl 1291.35242

Summary: The inviscid limit problem for the smooth solutions of the Boussinesq system is studied in this paper. We prove the \(H^s\) convergence result of this system as the diffusion and the viscosity coefficients vanish with the initial data belonging to \(H^s\). Moreover, the \(H^s\) convergence rate is given if we allow more regularity on the initial data.

MSC:

35Q35 PDEs in connection with fluid mechanics
35B25 Singular perturbations in context of PDEs
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