1. CJM 2012 (vol 64 pp. 1415)
|Global Well-Posedness and Convergence Results for 3D-Regularized Boussinesq System|
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, ArselÃ -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
Categories:35A05, 76D03, 35B40, 35B10, 86A05, 86A10