Nonlinear and oblique boundary value problems for the Stokes equations
Hamid Benseridi, Mourad Dilmi · Electronic journal of qualitative theory of differential equations · 2011
Abstract. 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. We first establish the existence result and some estimates for weak solutions of its approached problem. A specific regularity of the velocity and the pressure are obtained. The proof is based on the approach of maximal monotone graph by its Yosida regularization and the contraction method.