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 regularizing Boussinesq system, existence and uniqueness of weak solution, convergence results, compactness method in frequency space

MSC Classifications:

35A05, 76D03, 35B40, 35B10, 86A05, 86A10 show english descriptions General existence and uniqueness theorems
Existence, uniqueness, and regularity theory [See also 35Q30]
Asymptotic behavior of solutions
Periodic solutions
Hydrology, hydrography, oceanography [See also 76Bxx, 76E20, 76Q05, 76Rxx, 76U05]
Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05] 35A05 - General existence and uniqueness theorems
76D03 - 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]

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