Asymptotic behavior for stationary Navier-Stokes equations

Abstract

In this paper, we investigate the asymptotic behavior of solutions to the axisymmetric stationary Navier-Stokes equations. We assume that the flow is periodic in $x_3$-direction and has no swirl. Under the general integrability condition, we prove the pointwise decay estimate of the vorticity ω and obtain the Liouville-type theorem.