A new class of elliptic quasi-variational-hemivariational inequalities for fluid flow with mixed boundary conditions

In this paper we study a class of quasi-variational-hemivariational inequalities in reflexive Banach spaces. The contain convex potential, locally Lipschitz superpotential, and implicit obstacle set constraints. Solution existence compactness the solution to inequality problem are established based on Kakutani–Ky Fan fixed point theorem. applicability results is illustrated by steady-state Oseen model generalized Newtonian incompressible fluid with mixed boundary conditions. latter involve unilateral condition, Navier slip nonmonotone version nonlinear Navier-Fujita generalization threshold leak condition frictional type.