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# Global Well-Posedness and Convergence Results for 3D-Regularized Boussinesq System

Published:2012-08-25
Printed: Dec 2012
• Ridha Selmi,
Mathematics Department, Faculty of Sciences of Gabès, University of Gabès, Cité Erriadh, 6072 Zrig, Gabès, TUNISIA
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## Abstract

Analytical study to the regularization of the Boussinesq system is performed in frequency space using Fourier theory. Existence and uniqueness of weak solution with minimum regularity requirement are proved. Convergence results of the unique weak solution of the regularized Boussinesq system to a weak Leray-Hopf solution of the Boussinesq system are established as the regularizing parameter $\alpha$ vanishes. The proofs are done in the frequency space and use energy methods, Arselà-Ascoli compactness theorem and a Friedrichs like approximation scheme.
 Keywords: regularizing Boussinesq system, existence and uniqueness of weak solution, convergence results, compactness method in frequency space
 MSC Classifications: 35A05 - General existence and uniqueness theorems76D03 - Existence, uniqueness, and regularity theory [See also 35Q30] 35B40 - Asymptotic behavior of solutions 35B10 - Periodic solutions 86A05 - Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05] 86A10 - Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05]