Stability for the 2D incompressible MHD equations with only magnetic diffusion

TL;DR

This paper proves the global stability of solutions near a background magnetic field for the 2D incompressible MHD equations with magnetic diffusion, demonstrating the stabilizing effect of magnetic fields and providing explicit decay rates.

Contribution

It establishes a global stability result for the 2D incompressible MHD equations with magnetic diffusion, highlighting the magnetic field's stabilizing influence and deriving decay rates.

Findings

Global stability near background magnetic field

Explicit large-time decay rates

Magnetic field stabilizes electrically conducting fluids

Abstract

This paper presents a global stability result on perturbations near a background magnetic field to the 2D incompressible magnetohydrodynamic (MHD) equations with only magnetic diffusion on the periodic domain. The stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit large-time decay rate of the solutions.