A generalized Stokes system with a nonsmooth slip boundary condition

A class of quasi-variational-hemivariational inequalities in reflexive Banach spaces is studied. The inequalities contain a convex potential, a locally Lipschitz superpotential, and an implicit obstacle set of constraints. Results on the well posedness are established including existence, uniqueness, dependence of solution on the data, and the compactness of the solution set in the strong topology. The applicability of the results is illustrated by the steady-state Stokes model of a generalized Newtonian incompressible fluid with a nonmonotone slip boundary condition.