HOMOGENIZATION AND TWO-SCALE CONVERGENCE FOR A STOKES OR NAVIER-STOKES FLOW IN AN ELASTIC THIN POROUS MEDIUM

Abstract

In the general framework of the homogenization method we study the behavior of a thin elastic periodic structure immersed in a viscous fluid. After the proof of the convergence of the homogenization process by using the two-scale convergence method it is possible to take the limit as δ→0, the small parameter which represents the thickness of the solid part. We obtain a viscoelastic medium with fading memory. We consider two cases: the one in which we have a Stokes flow in the fluid part and the other one when we have a Navier-Stokes flow in the fluid part.