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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| Accès en ligne: | https://arxiv.org/abs/2401.00417 |
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| _version_ | 1866911787619713024 |
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| author | Ding, Shijin Lin, Zhilin |
| author_facet | Ding, Shijin Lin, Zhilin |
| contents | In this paper, we study the stability for 2-D plane Poiseuille flow $(1-y^2,0)$ in a channel $\mathbb{T}\times (-1,1)$ with Navier-slip boundary condition. We prove that if the initial perturbation for velocity field $u_0$ satisfies that $\|u_0\|_{H^{\frac{7}{2}+}} \leq ε_1 ν^{2/3}$ for some suitable small $0<ε_1 \ll 1$ independent of viscosity coefficient $ν$, then the solution to the Navier-Stokes equations is global in time and does not transit from the plane Poiseuille flow. This result improves the result of \cite{DL1} from $3/4$ to $2/3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00417 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stability for the 2-D plane Poiseuille flow in finite channel Ding, Shijin Lin, Zhilin Analysis of PDEs In this paper, we study the stability for 2-D plane Poiseuille flow $(1-y^2,0)$ in a channel $\mathbb{T}\times (-1,1)$ with Navier-slip boundary condition. We prove that if the initial perturbation for velocity field $u_0$ satisfies that $\|u_0\|_{H^{\frac{7}{2}+}} \leq ε_1 ν^{2/3}$ for some suitable small $0<ε_1 \ll 1$ independent of viscosity coefficient $ν$, then the solution to the Navier-Stokes equations is global in time and does not transit from the plane Poiseuille flow. This result improves the result of \cite{DL1} from $3/4$ to $2/3$. |
| title | Stability for the 2-D plane Poiseuille flow in finite channel |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.00417 |