Global well-posedness of the 3D Primitive Equations with magnetic field

TL;DR

This paper proves the global existence and uniqueness of strong solutions for the 3D primitive equations with magnetic field on a thin domain, without smallness restrictions on initial data, advancing understanding of magnetohydrodynamic flows.

Contribution

It establishes the first global well-posedness result for the 3D primitive equations with magnetic field without initial data restrictions.

Findings

Global existence and uniqueness of strong solutions

Solutions exist for any H^2-smooth initial data

No smallness assumption required on initial data

Abstract

In this paper, the three-dimensional primitive equations with magnetic field (PEM) are considered on a thin domain. We showed the global existence and uniqueness (regularity) of strong solutions to the three-dimensional incompressible PEM without any small assumption on the initial data. More precisely, there exists a unique strong solution globally in time for any given $H^2$-smooth initial data.