Optimal conduit shape for Stokes flow

Abstract

We consider the problem of the optimal shape of a two dimensional duct which contains a fluid governed by the Stokes equations with mixed boundary conditions. The conduit domain is assumed to be non-smooth and perturbations are allowed only on the walls, while the objective functional aims at minimizing the head loss and to enforce a uniform velocity profile at the outlet. We show existence of solutions to the shape optimization problem and determine the existence of the shape derivative.