A global existence result for the anisotropic magnetohydrodynamical systems

TL;DR

This paper proves the global existence of strong solutions for an anisotropic magnetohydrodynamics system in three dimensions, under conditions of fast rotation and small horizontal diffusivity, using Strichartz estimates.

Contribution

It establishes the global existence and uniqueness of solutions for an anisotropic MHD system with minimal vertical diffusivity, extending previous results to large initial data under rapid rotation.

Findings

Global existence of solutions for large initial data

Use of Strichartz estimates in MHD analysis

Conditions on rotation speed and diffusivity

Abstract

We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size $\epsilon$$\alpha$ with 0 \textless{} $\alpha$ $\le$ $\alpha$0, for some $\alpha$0 \textgreater{} 0). We prove the local existence and uniqueness of a strong solution and then, using Strichartz-type estimates, we prove that this solution globally exists in time for large initial data, when the rotation is fast enough.