Improved stability threshold for 2D Navier-Stokes Couette flow in an infinite channel
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908516574298112 |
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| author | Liang, Tao Wu, Jiahong Zhai, Xiaoping |
| author_facet | Liang, Tao Wu, Jiahong Zhai, Xiaoping |
| contents | We study the nonlinear stability of the two-dimensional Navier-Stokes equations around the Couette shear flow in the channel domain $\mathbb{R}\times[-1,1]$ subject to Navier slip boundary conditions. We establish a quantitative stability threshold for perturbations of the initial vorticity $ω_{in}$, showing that stability holds for perturbations of order $ν^{1/2}$ measured in an anisotropic Sobolev space. This sharpens the recent work of Arbon and Bedrossian [Comm. Math. Phys., 406 (2025), Paper No. 129] who proved stability under the threshold $ν^{1/2}(1+\ln(1/ν))^{-1/2}$. Our result removes the logarithmic loss and identifies the natural scaling $ν^{1/2}$ as the critical size of perturbations for nonlinear stability in this setting. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00694 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Improved stability threshold for 2D Navier-Stokes Couette flow in an infinite channel Liang, Tao Wu, Jiahong Zhai, Xiaoping Analysis of PDEs We study the nonlinear stability of the two-dimensional Navier-Stokes equations around the Couette shear flow in the channel domain $\mathbb{R}\times[-1,1]$ subject to Navier slip boundary conditions. We establish a quantitative stability threshold for perturbations of the initial vorticity $ω_{in}$, showing that stability holds for perturbations of order $ν^{1/2}$ measured in an anisotropic Sobolev space. This sharpens the recent work of Arbon and Bedrossian [Comm. Math. Phys., 406 (2025), Paper No. 129] who proved stability under the threshold $ν^{1/2}(1+\ln(1/ν))^{-1/2}$. Our result removes the logarithmic loss and identifies the natural scaling $ν^{1/2}$ as the critical size of perturbations for nonlinear stability in this setting. |
| title | Improved stability threshold for 2D Navier-Stokes Couette flow in an infinite channel |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.00694 |