Geodesic
Global Well-Posedness and Convergence Results for the 3D-Regularized Boussinesq System
Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1415-1435

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DOI

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.
DOI : 10.4153/CJM-2012-013-5
Mots-clés : 35A05, 76D03, 35B40, 35B10, 86A05, 86A10, regularizing Boussinesq system, existence and uniqueness of weak solution, convergence results, compactness method in frequency space 
Selmi, Ridha. Global Well-Posedness and Convergence Results for the 3D-Regularized Boussinesq System. Canadian journal of mathematics, Tome 64 (2012) no. 6, pp. 1415-1435. doi: 10.4153/CJM-2012-013-5
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     title = {Global {Well-Posedness} and {Convergence} {Results} for the {3D-Regularized} {Boussinesq} {System}},
     journal = {Canadian journal of mathematics},
     pages = {1415--1435},
     year = {2012},
     volume = {64},
     number = {6},
     doi = {10.4153/CJM-2012-013-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2012-013-5/}
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