Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Horizontal Eddy Diffusivity

TL;DR

This paper proves the global existence and uniqueness of strong solutions for the 3D primitive equations modeling oceanic and atmospheric flows, with only horizontal diffusion in temperature, using $H^2$ initial data.

Contribution

It establishes the global well-posedness of strong solutions for the 3D primitive equations with horizontal eddy diffusivity, a case previously not fully understood.

Findings

Global well-posedness of strong solutions is proven.

Solutions exist for all time with $H^2$ initial data.

The analysis handles equations with only horizontal diffusion.

Abstract

In this paper, we consider the initial-boundary value problem of the 3D primitive equations for oceanic and atmospheric dynamics with only horizontal diffusion in the temperature equation. Global well-posedness of strong solutions are established with $H^2$ initial data.