The usual formulation of the well-studied sliding plate problem of driven cavity flow involves an unphysical boundary velocity discontinuity at the corners where moving and fixed boundary surfaces intersect. Molecular dynamics simulations of a Lennard-Jones liquid in a cavity driven by the motion of realistic atomic walls at several Reynolds numbers are used to explore the small-scale structure of this flow. The results indicate that slip occurs in the corner region, removing the stress singularity which would otherwise occur, and furthermore that the fluid has non-Newtonian behavior there. Elsewhere, at least at low Reynolds numbers, the overall flow field is consistent with continuum calculations which do not allow for slip. As the Reynolds number increases, the slip region grows in size, and eventually extends across the entire moving boundary. The often-cited Navier slip boundary condition is shown to be incorrect. The mechanism for the avoidance of singular behavior here is generally similar to that of the moving contact line case.