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

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.

15 pages

References in corpus (2)

• Decay and vanishing of some D-solutions of the Navier-Stokes equations
• On convergence of arbitrary D-solution of steady Navier--Stokes system in 2D exterior domains