Hadamard variational formula for the Green function of the Stokes equations under the general second order perturbation
Erika Ushikoshi · Journal of the Mathematical Society of Japan · 2016
We consider the Hadamard variational formula for the Green function of the Stokes equations with the Dirichlet boundary condition under the smooth perturbation without assuming the volume preserving property. We establish the formula for the first and the second variation for the second order perturbation.