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

Published online by Cambridge University Press:  20 November 2018

Ridha Selmi
Ridha Selmi*
Affiliation:
Mathematics Department, Faculty of Sciences of Gabés, University of Gabés, Cité Erriadh, 6072 Zrig, Gabés, Tunisia and PDEs and Applications Lab, Faculty of Sciences of Tunis, University of Tunis El Manar, Campus Universitaire, 2092 El Manar, Tunis, Tunisia email: ridha.selmi@isi.rnu.tn
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Abstract

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Analytical study of the regularization of the Boussinesq system is performed in frequency space using Fourier theory. Existence and uniqueness of weak solutions 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, the Arselà-Ascoli compactness theorem and a Friedrichs-like approximation scheme.

Keywords

35A0576D0335B4035B1086A0586A10regularizing Boussinesq systemexistence and uniqueness of weak solutionconvergence resultscompactness method in frequency space
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 64 , Issue 6 , 01 December 2012 , pp. 1415 - 1435
Copyright
Copyright © Canadian Mathematical Society 2012

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