2023•arXiv (Cornell University)Open access

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

Xiaoping Zhai

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.

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Key concepts: Magnetohydrodynamic drive, Magnetohydrodynamics, Compressibility, Magnetic field, Physics, Stability (learning theory), Mechanics, Diffusion