  Molecular dynamics (MD) simulations have been carried out to investigate the
slip of fluid in the lid driven cavity flow where the no-slip boundary
condition causes unphysical stress divergence. The MD results not only show the
existence of fluid slip but also verify the validity of the Navier slip
boundary condition. To better understand the fluid slip in this problem, a
continuum hydrodynamic model has been formulated based upon the MD verification
of the Navier boundary condition and the Newtonian stress. Our model has no
adjustable parameter because all the material parameters (density, viscosity,
and slip length) are directly determined from MD simulations. Steady-state
velocity fields from continuum calculations are in quantitative agreement with
those from MD simulations, from the molecular-scale structure to the global
flow. The main discovery is as follows. In the immediate vicinity of the
corners where moving and fixed solid surfaces intersect, there is a core
partial-slip region where the slippage is large at the moving solid surface and
decays away from the intersection quickly. In particular, the structure of this
core region is nearly independent of the system size. On the other hand, for
sufficiently large system, an additional partial-slip region appears where the
slippage varies as $1/r$ with $r$ denoting the distance from the corner along
the moving solid surface. The existence of this wide power-law region is in
accordance with the asymptotic $1/r$ variation of stress and the Navier
boundary condition.
