On Shape Stability of Incompressible Fluids Subject to Navier's Slip Condition

The paper is concerned with the equations of motion for incompressible fluids that slip at the wall. Particular interest is in the domain dependence of weak solutions. We prove that the solutions depend continuously on the perturbation of the boundary provided that the latter remains in the class . The result is applicable to a wide class of shape optimization problems and is optimal in terms of boundary regularity.