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

Xiaoping Zhai

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arXiv · 2307.12197

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

Xiaoping Zhai

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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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Xiaoping Zhai. 2023-07-23. Stability for the 2D incompressible MHD equations with only magnetic diffusion. https://arxiv.org/abs/2307.12197

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