Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition

Fuente: arXiv
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Hauptverfasser: Kozono, Hideo, Terasawa, Yutaka, Wakasugi, Yuta
Format: Preprint
Veröffentlicht: 2022
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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