ABSTRACT
A shape optimization problem for viscous incompressible flow is studied. The goal is to find a shape of the part of the boundary of the flow region, so that the given force field is produced there. The variable domain problem is relaxed so that it becomes a nonsmooth optimization problem on the fixed domain for the Navier-Stokes system with somewhat singular right-hand side. This formulation is useful for flows of highly viscous materials or in the case where we are not too far off-design.
