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arXiv · 2409.00307

Boundary driven instabilities of Couette flows

Dongfen Bian·Emmanuel Grenier·Nader Masmoudi·Weiren Zhao
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Abstract

In this article, we prove that the threshold of instability of the classical Couette flow in $H^s$ for large $s$ is $\nu^{1/2}$. The instability is completely driven by the boundary. The dynamic of the flow creates a Prandtl type boundary layer of width $\nu^{1/2}$ which is itself linearly unstable. This leads to a secondary instability which in turn creates a sub-layer.

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Dongfen Bian, Emmanuel Grenier, Nader Masmoudi, Weiren Zhao. 2024-08-31. Boundary driven instabilities of Couette flows. https://arxiv.org/abs/2409.00307

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