We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is completely nonlinear and is due to some energy cascade. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

中文翻译：

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低Gevrey空间中库埃特流的长期不稳定性

如果扰动不如 2 类 Gevrey 空间平滑，我们证明了 Couette 流的不稳定性。这表明这是该问题的关键规律，因为在 [5] 中证明了扰动的稳定性和无粘阻尼成立：比 2 类 Gevrey 空间更平滑。一个很大的新颖之处在于，这个临界空间是由完全非线性的不稳定机制引起的，并且是由一些能量级联引起的。© 2023 作者。《纯粹数学与应用数学通讯》由 Wiley periodicals LLC 出版。