This paper is concerned with a stability problem on perturbations near a physically important steady state solution of the 3D MHD system. We obtain three major results. The first assesses the existence of global solutions with small initial data. Second, we derive the temporal decay estimate of the solution in the L²-norm, where to prove the result, we need to overcome the difficulty caused by the presence of linear terms from perturbation. Finally, the decay rate in L² space for higher order derivatives of the solution is established.

中文翻译：

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接近平衡的 3D 磁流体动力学方程的稳定性问题

本文关注的是 3D MHD 系统物理上重要的稳态解附近扰动的稳定性问题。我们获得了三个主要结果。第一个评估具有少量初始数据的全局解决方案的存在。其次，我们在L ^{2 -}范数中推导出解的时间衰减估计，为了证明结果，我们需要克服由扰动线性项的存在引起的困难。最后，确定解的高阶导数在L ²空间中的衰减率。