  We consider the steady Navier-Stokes system with mixed boundary conditions,
in subdomains of a holdall domain. We study, via the penalization method, its
approximation properties. Error estimates, obtained using the extension
operator, other evaluations and the uniqueness of the solution, when the
viscosity may be arbitrarily small in certain subdomains, are also discussed.
Numerical tests, including topological optimization applications, are
presented. A general convergence result for the approximation of this type of
geometric inverse problems and of the associated optimal control problems, is
investigated in the last part of the paper.
