  This paper is concerned with a shape sensitivity analysis of a viscous
incompressible fluid driven by Stokes equations with nonhomogeneous boundary
condition. The structure of shape gradient with respect to the shape of the
variable domain for a given cost function is established by using the
differentiability of a minimax formulation involving a Lagrangian functional
combining with function space parametrization technique or function space
embedding technique. We apply an gradient type algorithm to our problem.
Numerical examples show that our theory is useful for practical purpose and the
proposed algorithm is feasible.
