Existence and regularity results for the primitive equations in two space dimensions (Q1429990)

The aim of this article is to present various results of existence, uniqueness and regularity of solutions for the Primitive Equations of the ocean (PEs) in two space dimensions with periodic boundary conditions. First by recalling the variational formulation of the envisaged problem under suitable assumptions the existence of weak solutions for the PEs is proved. Then by deriving the necessary a priori estimates the authors also prove the existence and uniqueness of strong solutions and the existence of more regular solutions, up to \(C^\infty\) regularity.