# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1901.01384