  In this paper we study existence, dependence and optimal control results
concerning solutions to a class of hemivariational inequalities for stationary
Navier-Stokes equations but without making use of the theory of pseudo-monotone
operators. To do so, we consider a classical assumption, due to J. Rauch, which
constrains us to make a slight change on the definition of a solution. The
Rauch assumption,, although insure the existence of a solution, does not allow
the conclusion that the non-convex functional is locally Lipschitz. Moreover,
two dependence results are proved, one with respect to changes of the boundary
condition and the other with respect to the density of external forces. The
later one will be used to prove the existence of an optimal control to the
distributed parameter optimal control problem where the control is represented
by the external forces.
