Homogenization of the Stokes Problem With Non-homogeneous Slip Boundary Conditions

Abstract

We study the Stokes system with non-homogeneous Fourier boundary conditions depending on a parameter, in a domain with periodic inclusions of the size of the period. Following the values of this parameter, we obtain at the limit a Darcy's law, a Brinkmann type equation or a Stokes type equation. We also present a physical model to which the results apply. This model describes the flow of an incompressible viscous fluid through a porous medium under the action of an exterior electric field.