Séance Séminaire

Séminaire ACSIOM

Homogenization problems in fluid mechanics.

I will talk about homogenization problems in fluid mechanics - the study of asymptotic behavior of fluid flows (governed by Stokes or Navier-Stokes equations) in domains perforated with a large number of tiny holes (or obstacles). A typical case of such domains is the so called porous media. With an increasing number of holes, the fluid flow approaches an effective state governed by certain ?homogenized? equations which are homogeneous in form (without obstacles). The homogenized equation (or limit equation) is crucially determined by the ratio between the size of the holes and the mutual distance of the holes. I this talk, I will introduce the background of this study and some known results. I will also recall my recent results in this field. At the end, I will present some open problems.