Sobolev and Gevrey regularity results for the primitive equations in three space dimensions

摘要

The aim of this article is to present a qualitative study of the Primitive Equations in a three-dimensional domain, with periodical boundary conditions. We start by recalling some already existing results regarding the existence locally in time of weak solutions and existence and uniqueness of strong solutions, and we prove the existence of very regular solutions, up to C{sup}∞-regularity. In the second part of the article we prove that the solution of the Primitive Equations belongs to a certain Gevrey class of functions.