Shape sensitivity analysis of time-dependent flows of incompressible   non-Newtonian fluids
  We study the shape differentiability of a cost function for the flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of the obstacle we express the shape gradient of the cost function which can be subsequently used to improve the initial design. 
Jan Sokolowski and Jan Stebel
math.AP math.OC