Global regular solutions to the Navier-Stokes equations in an axially symmetric domain (Q1039202)

The Navier-Stokes equations are considered in an axially symmetric domain in \(\mathbb{R}^3\) and with boundary slip conditions. It is assumed that initial angular component of velocity and angular component of the external force and angular derivatives of the cylindrical components of initial velocity and of the external force are sufficiently small in corresponding norms. Then the existence of global regular solutions is proved.