Abstract
In this paper, we study the three-dimensional Lagrangian averaged Boussinesq-a system which is a regularized version of the three-dimensional Boussines-alpha system. We prove the existence of a weak solution to the 3D-Lagrangian averaged Boussinesq-alpha system, in Sobolev spaces. Unlike preceding works, this solution is global in time and depends continuously on the initial data, in particular, it is unique. More importantly, it converges to a weak solution of the three-dimensional Boussinesq system, as the regularizing parameter alpha vanishes.