  For the non-stationary Stokes system, it is well-known that one can improve
spatial regularity in the interior, but not near the boundary if it is coupled
with the no-slip boundary condition. In this note we show that, to the
contrary, spatial regularity can be improved near a flat boundary if it is
coupled with the Navier boundary condition, with either infinite or finite slip
length. The case with finite slip length is more difficult than the case with
infinite slip length.
