Variational-hemivariational inequalities for Navier-Stokes equations with mixed boundary conditions

This paper presents elliptic variational-hemivariational inequalities, focusing on steady Navier-Stokes equations for generalized Newtonian incompressible fluid. It presents a variational-hemivariational inequality that links the Navier-Stokes equations with mixed boundary conditions. These conditions encompass unilateral, nonmonotone nonlinear slip, as well as nonlinear leak boundary conditions. The existence of weak solutions is established using a surjectivity result.