Axisymmetric flows in the exterior of a cylinder

Abstract

AbstractWe study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder$\Pi =\{x=(x_{h}, x_3)\ \vert \vert x_{h} \vert \gt 1\}$, 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$ru^{\theta }_{0}\in L^{\infty }(\Pi )$.