Global well-posedness and Large Time Asymptotic Behavior of Strong Solutions to the Cauchy Problem of the 2-D MHD equation

Abstract

This paper is concerned with the Cauchy problem of the two-dimensional MHD system with magnetic diffusion. It was proved that the MHD equations have a unique global strong solution around the equilibrium state $(0,e_1)$. Furthermore, the $L^2$ decay rate of the velocity and magnetic field is obtained.

Our proof is incomplete. We need to check it