Global well-posedness of the MHD equations in a homogeneous magnetic field

TL;DR

This paper proves the global well-posedness of magnetohydrodynamics equations with small, possibly unequal viscosity and resistivity in high-temperature plasma settings, given initial conditions near a homogeneous magnetic field.

Contribution

It establishes the global existence and uniqueness of solutions for the MHD equations under small initial perturbations in a weighted Hölder space, independent of dissipation coefficients.

Findings

Global well-posedness proven for MHD with small viscosity and resistivity

Results hold for initial conditions close to a homogeneous magnetic field

Closeness condition is independent of dissipation coefficients

Abstract

In this paper, we study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the initial velocity is close to 0 and the initial magnetic field is close to a homogeneous magnetic field in the weighted H\"{o}lder space, where the closeness is independent of the dissipation coefficients.