Viscous boundary-layer effects in nearly inviscid cylindrical flows

The dynamics of flow inside a cylinder at high Reynolds number are considered. A study of the viscous boundary layer near the walls is performed. In the case where there is no pressure gradient, a result is proven demonstrating that a regular perturbation expansion holds for the solution, even when a small discontinuity exists in the wall data. In addition, the characteristic decay rate of the flow in the viscous boundary layer is established. In the case where there is a pressure gradient, a result is proven demonstrating that an additional scale, related to the size of the disturbance and larger than the boundary-layer width, must be used in a multiple-scale expansion. Examination of the divergence of these multiple-scale expansions for finite disturbances leads to discussions of viscous flow and separation processes. AMS classification scheme numbers: 76C05, 76D15, 76D30, 76F99, 76U05