  We consider two-dimensional nonstationary Navier-Stokes shear flow with
multivalued and nonmonotone boundary conditions on a part of the boundary of
the flow domain. We prove the existence of global in time solutions of the
considered problem which is governed by a partial differential inclusion with a
multivalued term in the form of Clarke subdifferential. Then we prove the
existence of a trajectory attractor and a weak global attractor for the
associated multivalued semiflow. This research is motivated by control problems
for fluid flows in domains with semipermeable walls and membranes.
