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arXiv · 2208.03850

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
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Abstract

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.

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Hideo Kozono, Yutaka Terasawa, Yuta Wakasugi. 2022-08-08. Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition. https://doi.org/10.1016/j.jde.2023.05.025

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