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

Abstract

AbstractAnalytical study of the regularization of the Boussinesq systemis 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 parameterαvanishes. The proofs are done in the frequency space and use energy methods, the Arselà-Ascoli compactness theorem and a Friedrichs-like approximation scheme.