Axisymmetric flows in the exterior of a cylinder

Abstract

We study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $\Pi =\{x=(x_h,x_3)||x_h|>1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^3\cap L^2(\Pi )$ satisfying the decay condition of the swirl component $r{u}_0^{\theta }\in L^{\infty }(\Pi )$.

Final version. The title is changed from "Axisymmetric flows in an exterior domain"