Steady flow of generalized Newtonian fluid with multivalued rheology and nonmonotone friction law

We study the stationary incompressible flow of a generalized Newtonian fluid described by a nonlinear multivalued maximal monotone constitutive law and a multivalued nonmonotone frictional boundary condition. We provide results on the existence and uniqueness of a solution to the variational form of the problem. When the multivalued laws are of a subdifferential form, we prove the existence of a solution to a variational-hemivariational inequality for the flow's velocity field.