New approach to the Hadamard variational formula for the Green function of the Stokes equations

作者：Ushikoshi Erika^*

来源：Manuscripta Mathematica, 2015, 146(1-2): 85-106.

DOI：10.1007/s00229-014-0695-5

We consider the Hadamard variational formula for the Green function of the Stokes equations which describes the motion of the incompressible fluid moving infinitesimally on the bounded domain Omega with the smooth boundary a,Omega. Under the perturbation with preserving its volume and keeping its topological type, we establish a more refined proof of its formula of the Green function not only for the first variation but also the second variation for both velocity and pressure. Our method gives a new systematic proof of the Hadamard variational formula, which enables us to deal with the higher derivatives with respect to the perturbation of domains.

• 出版日期2015-1