In this paper, we study the long-time behavior of the solution for the linearized ideal MHD around sheared velocity and magnetic field under Stern stability condition. We prove that the velocity and magnetic field will converge to sheared velocity and magnetic field as time approaches infinity. Moreover a new depletion phenomenon is proved: the horizontal velocity and magnetic field at the critical points will decay to 0 as time approaches infinity.

中文翻译：

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具有强剪切磁场的流动等离子体中的线性阻尼和耗尽

在本文中，我们研究了线性化理想 MHD 解在 Stern 稳定条件下围绕剪切速度和磁场的长期行为。我们证明了随着时间接近无穷大，速度和磁场将收敛到剪切速度和磁场。此外还证明了一种新的耗尽现象：随着时间接近无穷大，临界点的水平速度和磁场将衰减到0。