Abstract
Analytical study to an alpha‐regularization of the Boussinesq system is performed using Fourier theory. Existence and uniqueness of strong solution are proved. Convergence results of the unique strong solution for the regularized Boussinesq system to the unique strong solution for the Boussinesq system are established as the regularizing parameter vanishes. The proofs are performed in the frequency space. We use energy methods, Friedrichs's approximation scheme, and Arselà–Ascoli compactness theorem. Copyright © 2016 John Wiley & Sons, Ltd.
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