A fixed point approach to the semi-linear Stokes problem

Abstract

"The aim of this paper is to study the Dirichlet problem for semi-linear Stokes equations. The approach of this study is based on the operator method, using abstract results of nonlinear functional analysis. We rst study the problem using Schauder's fixed point theorem and we prove the existence of a solution in case that the nonlinear term has a linear growth. Next we establish whether the existence of solutions can still be obtained without this linear growth restriction. Such a result is obtained by applying the Leray-Schauder fixed point theorem."