标题： 关于粘性三维旋转库埃特流的稳定性 显示英文标题

标题： On the stability of viscous three-dimensional rotating Couette flow

摘要： 我们研究了在旋转作用下（由科里奥利力给出）三维纳维-斯托克斯方程中库埃特流的稳定性。在此情况下，靠近库埃特流的线性化动力学的性质关键取决于背景剪切与旋转之间的力平衡，其中包括升力或指数不稳定性，以及一个稳定区域。在后者中，剪切或旋转惯性波导致混合和色散效应，这些效应对于不同的动力学领域是相关的。我们的主要结果通过线性和非线性情形下的增强耗散和色散振幅衰减来量化这些效应：特别是，我们建立了一个非线性过渡阈值，该阈值在没有旋转的情况下得到了定量改进（并且随着旋转速度的增加而进一步增加），展示了其稳定作用。 显示英文摘要

摘要： We study the stability of Couette flow in the 3d Navier-Stokes equations with rotation, as given by the Coriolis force. Hereby, the nature of linearized dynamics near Couette flow depends crucially on the force balance between background shearing and rotation, and includes lift-up or exponential instabilities, as well as a stable regime. In the latter, shearing resp. rotational inertial waves give rise to mixing and dispersive effects, which are relevant for distinct dynamical realms. Our main result quantifies these effects through enhanced dissipation and dispersive amplitude decay in both linear and nonlinear settings: in particular, we establish a nonlinear transition threshold which quantitatively improves over the setting without rotation (and increases further with rotation speed), showcasing its stabilizing effect.