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

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.