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In this paper we study existence, dependence and optimal control resultsconcerning solutions to a class of hemivariational inequalities for stationaryNavier-Stokes equations but without making use of the theory of pseudo-monotoneoperators. To do so, we consider a classical assumption, due to J. Rauch, whichconstrains us to make a slight change on the definition of a solution. TheRauch assumption,, although insure the existence of a solution, does not allowthe conclusion that the non-convex functional is locally Lipschitz. Moreover,two dependence results are proved, one with respect to changes of the boundarycondition and the other with respect to the density of external forces. Thelater one will be used to prove the existence of an optimal control to thedistributed parameter optimal control problem where the control is representedby the external forces.

Hemivariational inequality for stationary Navier-Stokes equations: existence, dependence and optimal control