A fixed point approach to the semi-linear Stokes problem
DOI:
https://doi.org/10.24193/subbmath.2023.3.08Keywords:
Stokes system, semi-linear problem, operator method, fixed point theo- rem, Sobolev space.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 first 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.
Mathematics Subject Classification (2010): 35Q30, 35J25, 35J61, 35Q35.
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