Stability threshold of the two-dimensional Couette flow in the whole plane
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915109909037056 |
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| author | Li, Hui Liu, Ning Zhao, Weiren |
| author_facet | Li, Hui Liu, Ning Zhao, Weiren |
| contents | 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 $ν^{\frac{1}{2}}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_10818 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability threshold of the two-dimensional Couette flow in the whole plane Li, Hui Liu, Ning Zhao, Weiren Analysis of PDEs 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 $ν^{\frac{1}{2}}$. |
| title | Stability threshold of the two-dimensional Couette flow in the whole plane |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.10818 |