Strong Solutions To 3d-Lagrangian Averaged Boussinesq System

Under suitable assumptions on the initial data, we prove the existence, uniqueness of the strong solutions to a regularized periodic three-dimensional Lagrangian averaged Boussinesq system, in a Sobolev spaces. Also, we establish the convergence results of this unique strong solution of this regularized Boussinesq system to a strong solution of the three-dimensional Boussinesq system, as the regularizing parameter vanishes.