In this note, we are concerned with uniform stability for a Leray–Hopf weak solution of the MHD equations and obtain that the Leray–Hopf weak solution is uniformly stable with respect to a small perturbation of initial velocity, magnetic and external forcing. This extends and improves the results given by Gallagher–Planchon and Dong–Jia for Navier–Stokes equations.

中文翻译：

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3D 磁流体动力学方程的均匀稳定性

在本笔记中，我们关注 MHD 方程的 Leray-Hopf 弱解的均匀稳定性，并获得 Leray-Hopf 弱解相对于初始速度、磁力和外力的小扰动是均匀稳定的。这扩展并改进了 Gallagher-Planchon 和 Dong-Jia 为 Navier-Stokes 方程给出的结果。