On incompressible viscous fluid flows with slip boundary conditions

We consider stationary and nonstationary problems of viscous incompressible fluid flows with slip boundary conditions in a rotating bounded domain. We show a geometrical representation of the slip conditions where principal curvatures of its boundary surfaces are characteristic coefficients. When the domain is axisymmetric, it is proved that a steady flow exists if external force f→ in equations of motion is orthogonal to rigid rotational flows, and that a nonstationary flow converges to a steady flow depending on its initial flow as time tends to infinity, if f→ is independent of time and orthogonal to rigid rotational flows and if the L2-norm of f→ is sufficiently small.