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

TL;DR

This paper proves the global existence and uniqueness of strong solutions to the 2-D MHD equations with magnetic diffusion, and analyzes their decay behavior over time.

Contribution

It establishes the global well-posedness of strong solutions for the 2-D MHD system with magnetic diffusion and determines their decay rates.

Findings

Unique global strong solution around equilibrium state

Decay rate of velocity and magnetic field in L^2 norm

Results applicable to 2-D MHD system with magnetic diffusion

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.