Some mathematical properties of the planetary geostrophic equations for large-scale ocean circulation

We study in this article the well-posdness of the planetary geostrophic equations of the gyre-scale midlatitude ocean, and address in particular the question of the existence and some properties of global (in time) weak solutions of the planetary geostrophic equations of the gyre-scale midlatitude ocean. The main objective is to study effects of different friction and diffusion terms and to propose and to analyze proper boundary conditions for the correspondi models. Several open questions are also indicated.