Nonlinear and oblique boundary value problems for the Stokes equations

In this paper we consider the nonlinear boundary value problem governed by a stationary perturbed Stokes system with mixed boundary conditions (Dirichlet- maximal monotone graph), in a smooth domain. Existence and regularity of the weak solution to this problem are proved. The proof is based on the approach of maximal monotone graph by its Yosida regularization and the contraction method.