On the primitive equations and the hydrostatic Stokes operator

The primitive equations for the atmosphere and ocean, as well as its linearization, called the hydrostatic Stokes equation, are considered. The study of the latter problem in spaces of Lp- and anisotropic Lp-type yields results such as parabolic decay estimates as well as the property of maximal regularity. Applying these results to the full nonlinear problem yields the existence of unique global strong solutions to the primitive equations for a large class of initial data