Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866913259025596416 |
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| author | Kozono, Hideo Terasawa, Yutaka Wakasugi, Yuta |
| author_facet | Kozono, Hideo Terasawa, Yutaka Wakasugi, Yuta |
| contents | We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in $\mathbb{R}^3$. We assume that the flow is periodic in $x_3$-direction and has no swirl. This problem is closely related with two-dimensional exterior problem. Under a condition on the generalized finite Dirichlet integral, we give a pointwise decay estimate of the vorticity at the spatial infinity. Moreover, we prove a Liouville-type theorem only from the condition of the generalized finite Dirichlet integral. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_03850 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition Kozono, Hideo Terasawa, Yutaka Wakasugi, Yuta Analysis of PDEs 35Q30, 35B53, 76D05 We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in $\mathbb{R}^3$. We assume that the flow is periodic in $x_3$-direction and has no swirl. This problem is closely related with two-dimensional exterior problem. Under a condition on the generalized finite Dirichlet integral, we give a pointwise decay estimate of the vorticity at the spatial infinity. Moreover, we prove a Liouville-type theorem only from the condition of the generalized finite Dirichlet integral. |
| title | Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition |
| topic | Analysis of PDEs 35Q30, 35B53, 76D05 |
| url | https://arxiv.org/abs/2208.03850 |