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

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