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| Autori principali: | , , , |
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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2310.11694 |
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| _version_ | 1866916114009686016 |
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| author | Chen, Qi Ding, Shijin Lin, Zhilin Zhang, Zhifei |
| author_facet | Chen, Qi Ding, Shijin Lin, Zhilin Zhang, Zhifei |
| contents | In this paper, we study the nonlinear stability for the 3-D plane Poiseuille flow $(1-y^2,0,0)$ at high Reynolds number $Re$ in a finite channel $\mathbb{T}\times [-1,1 ]\times \mathbb{T}$ with non-slip boundary condition. We prove that if the initial velocity $v_0$ satisfies $\|v_0-(1-y^2,0,0)\|_{H^{4}}\leq c_0 Re^{-\frac{7}{4}}$ for some $c_0>0$ independent of $Re$, then the solution of 3-D Naiver-Stokes equations is global in time and does not transit away from the plane Poiseuille flow. To our knowledge, this is the first nonlinear stability result for the 3-D plane Poiseuille flow and the transition threshold is accordant with the numerical result by Lundbladh et al. \cite{LHR}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11694 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Nonlinear stability for 3-D plane Poiseuille flow in a finite channel Chen, Qi Ding, Shijin Lin, Zhilin Zhang, Zhifei Analysis of PDEs In this paper, we study the nonlinear stability for the 3-D plane Poiseuille flow $(1-y^2,0,0)$ at high Reynolds number $Re$ in a finite channel $\mathbb{T}\times [-1,1 ]\times \mathbb{T}$ with non-slip boundary condition. We prove that if the initial velocity $v_0$ satisfies $\|v_0-(1-y^2,0,0)\|_{H^{4}}\leq c_0 Re^{-\frac{7}{4}}$ for some $c_0>0$ independent of $Re$, then the solution of 3-D Naiver-Stokes equations is global in time and does not transit away from the plane Poiseuille flow. To our knowledge, this is the first nonlinear stability result for the 3-D plane Poiseuille flow and the transition threshold is accordant with the numerical result by Lundbladh et al. \cite{LHR}. |
| title | Nonlinear stability for 3-D plane Poiseuille flow in a finite channel |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.11694 |