Global regularity to the 3D MHD equations with large initial data in bounded domains

Abstract

This paper considers the global regularity to the 3D incompressible MHD equations with large initial data in bounded domains. Let μ, ν, u, and b denote the viscosity coefficient, magnetic diffusivity, velocity field, and magnetic field, respectively. We construct new systems for (u − b) and (u + b) to overcome the difficulties caused by the large initial data. It is shown that (u,b)H1 is globally bounded as long as (u0−b0)H1+μ−ν(μ+ν)−1 or (u0+b0)H1+μ−ν(μ+ν)−1 is sufficiently small, which indicates that the Navier-Stokes equations can be regularized by the magnetic field.