Stability threshold of the two-dimensional Couette flow in the whole plane

Hui Li; Ning Liu; Weiren Zhao

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arXiv · 2501.10818

Stability threshold of the two-dimensional Couette flow in the whole plane

Hui Li·Ning Liu·Weiren Zhao

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Abstract

In this paper, we study the stability threshold for the two-dimensional Couette flow in the whole plane. Our main result establishes that the asymptotic stability threshold is at most $\frac{1}{3}+$ for Sobolev perturbations with additional control over low horizontal frequencies, aligning with the threshold results in periodic domains. As a secondary outcome of our approach, we also prove the asymptotic stability for perturbations in weak Sobolev regularity with size $\nu^{\frac{1}{2}}$.

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Hui Li, Ning Liu, Weiren Zhao. 2025-01-18. Stability threshold of the two-dimensional Couette flow in the whole plane. https://arxiv.org/abs/2501.10818

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