  In this paper we study non stationary viscous incompressible fluid flows with
nonlinear boundary slip conditions given by a subdifferential property of
friction type. More precisely we assume that the tangential velocity vanishes
as long as the shear stress remains below a threshold, that may depend on the
time and the position variables but also on the stress tensor, allowing to
consider Coulomb's type friction laws. An existence and uniqueness theorem is
obtained first when the shear stress threshold is a data and sharp estimates
are derived for the velocity and pressure fields as well as for the stress
tensor. Then an existence result is proved for the non-local Coulomb's friction
case by using a successive approximation technique with respect to the shear
stress threshold.
