Global well-posedness to the 3D incompressible MHD equations with a new class of large initial data

Abstract

We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a byproduct, this result improves the corresponding result in \cite{HHW}. In addition, we also get the global result for this system in $\mathcal{\chi}^{-1}(\R^3)$ originally developed in \cite{LL}. More precisely, we only assume that the norm of initial data is exactly smaller than the sum of viscosity and diffusivity parameters.