... of the strong solutionsIn this section we will use the a priori estimates (58 )–( 79) to show the global existence and uniqueness, i.e. global regularity, of strong solutions to the system (26 )–( 31).Theorem ... (75), (77) and (79). Therefore T∗= ∞,and the solution (v, T) exists globally in time.Next, we show the continuous dependence on the initial data and the the uniqueness of the strong solutions. ... under the Boussinesq approximation. Moreover, and due to the shallowness of the oceansand the atmosphere, i.e., the depth of the fluid layer is very small in compar-ison to the radius of the earth,...