Axisymmetric flows in the exterior of a cylinder. Issue 4 (August 2020) - Abe, K.; Seregin, G.
Abstract: We study an initial-boundary value problem of the three-dimensional Navier-Stokes equations in the exterior of a cylinder $Π =\{x=(x_{h}, x_3)\ \vert \vert x_{h} \vert \gt 1\}$, subject to the slip boundary condition. We construct unique global solutions for axisymmetric initial data $u_0\in L^{3}\cap L^{2}(Π )$ satisfying the decay condition of the swirl component $ru^{θ }_{0}\in L^{∞ }(Π )$ .