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

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.

I have modified a typo in the main theorem. J. Differential Equations 374 (2023), 267-278