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

Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi

研究成果: ジャーナルへの寄稿学術論文査読

抄録

We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in R3. We assume that the flow is periodic in x3-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. This reveals the relation between the integrability of ∇v and the decay rate of ω near the spatial infinity. Moreover, we prove a Liouville-type theorem only from the condition of the generalized finite Dirichlet integral.

本文言語英語
ページ(範囲)905-926
ページ数22
ジャーナルJournal of Differential Equations
365
DOI
出版ステータス出版済み - 2023 8月 25

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