Global special regular solutions to the Navier-Stokes equations in a cylindrical domain without the axis of symmetry

Abstract

Global existence of regular solutions to the Navier-Stokes equations in a bounded cylindrical domain without the axis of symmetry and with boundary slip conditions is proved. We showed the existence of solutions without restrictions on the magnitude of the initial velocity assuming only that the $L_2$-norms of the angular derivative of the cylindrical components of the initial velocity and the external force are sufficiently small. To prove global existence some decay estimates on the external force are imposed.