Global well–posedness for the 3D primitive equations in anisotropic framework

Abstract

This paper is concerned with the initial–boundary value problem of the 3D primitive equations with only horizontal viscosities and horizontal diffusion. We first establish the local well–posedness result of this system, with the initial data belongs to the anisotropic Sobolev pace H0,s(s>12). Then, under the basic and high-order energy estimates, one can extend the local solution to the global one provided that s>1. The restrictions on the initial data is more weaker than the previous results which are obtained by Cao et al. ((2016) [8] and (2017) [9]), in which the initial data belongs to H2 and H1∩L∞, respectively.