Stability of Axially Symmetric Solutions to the Navier—Stokes Equations in Cylindrical Domains

Abstract

Using the result of O. A. Ladyzhenskaya [1], we establish the existence of a global solution, close to axially symmetric solutions, for the Navier-Stokes equations in a cylinder with boundary slip conditions. The solution belongs to a weight Sobolev space and possesses the property that the angular component of velocity, as well as the angular derivatives of cylindrical components of velocity and pressure, is sufficiently small. The uniqueness theorem is also established.