Global Solutions and Asymptotic Study to a 3D-Lagrangian Boussinesq System

Abstract

We prove that the Lagrangian-averaged​ 3D periodic Boussinesq system has a global in time weak solution that depends continuously on time. Also, we establish that a unique strong global in time solution exists. Moreover, we show that the system has a compact global attractor which is connected. The proofs are based on the energy methods and the absorbing balls technics. We utilize the coupling between the mean free temperature and the velocity field to close the energy estimates independently on time. This allows us to obtain global in time solutions and a global attractor.