Asymptotic stability of the symmetric flow via inviscid damping and enhanced dissipation
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908604480618496 |
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| author | Chen, Qi Li, Hao Shen, Shunlin Zhang, Zhifei |
| author_facet | Chen, Qi Li, Hao Shen, Shunlin Zhang, Zhifei |
| contents | In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the non-slip boundary condition. As an immediate consequence, we prove the asymptotic stability of the symmetric flow in the high Reynolds number regime. Namely, if the initial velocity perturbation $u^{\mathrm{in}}$ satisfies $\Vert u^{\mathrm{in}}-(U(y),0) \Vert_{H^5}\leq c ν^{\frac{2}{3}}$, then inviscid damping and enhanced dissipation estimates also hold for the solution to the Navier-Stokes system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability of the symmetric flow via inviscid damping and enhanced dissipation Chen, Qi Li, Hao Shen, Shunlin Zhang, Zhifei Analysis of PDEs In this paper, we establish the inviscid damping and enhanced dissipation estimates for the linearized Navier-Stokes system around the symmetric flow in a finite channel with the non-slip boundary condition. As an immediate consequence, we prove the asymptotic stability of the symmetric flow in the high Reynolds number regime. Namely, if the initial velocity perturbation $u^{\mathrm{in}}$ satisfies $\Vert u^{\mathrm{in}}-(U(y),0) \Vert_{H^5}\leq c ν^{\frac{2}{3}}$, then inviscid damping and enhanced dissipation estimates also hold for the solution to the Navier-Stokes system. |
| title | Asymptotic stability of the symmetric flow via inviscid damping and enhanced dissipation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.18361 |