A free discontinuity approach to optimal profiles in Stokes flows

In the talk I will consider the problem of finding the optimal shape of an obstacle which minimizes the drag force in an incompressible Stokes flow under Navier conditions at the boundary. I will propose a relaxation of the problem within the framework of free discontinuity problems, modeling the obstacle as a set of finite perimeter and the velocity field as a special function of bounded deformation (SBD): within this approach, the optimal obstacle may develop naturally geometric features of co-dimension 1.