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The stationary Stokes equations for a generalized Newtonian fluid with nonlinear unilateral, and slip and leak boundary conditions are investigated. Boundary conditions include the generalized Clarke gradient and the convex subdifferential, and the variational formulation of the problem is the variational–hemivariational inequality for the velocity field. Existence and uniqueness result for weak solution is proved by using a surjectivity theorem for a pseudomonotone perturbation of a maximal monotone operator.

Steady flow with unilateral and leak/slip boundary conditions by the Stokes variational–hemivariational inequality