The nanoscale cylindrical Couette flow is investigated by means of
molecular dynamics simulations, in the case where the inner cylinder
is rotating whereas the outer cylinder is at rest. We find that the
tangential velocity of the flow is inverted when the fluid-wall
interaction near the outer cylinder is weak and the fluid density is
low. The unusual velocity inversion behavior is shown to be strongly
related to the degree of the slip between the fluid and the outer
cylinder, which is determined by the presence or absence of the
layering of the fluid near the outer wall.