On the regularity of the primitive equations of the ocean

We prove the existence of global strong solutions of the primitive equations of the ocean in the case of the Dirichlet boundary conditions on the side and the bottom boundaries including the varying bottom topography. Previously, the existence of global strong solutions was known in the case of the Neumann boundary conditions in a cylindrical domain (Cao and Titi 2007 Ann. Math. 166 245–67).