IUMJ

Title: Hadamard variational formula for the Green function for the velocity and pressure of the Stokes equations

Authors: Erika Ushikoshi

Issue: Volume 62 (2013), Issue 4, 1315-1379

Abstract:

We consider the Hadamard variational formula for the Green function of the Stokes equations $\{\boldsymbol{G},R\}$ which describes the motion of the incompressible fluids moving slowly in the bounded domain $\Omega$ with the smooth boundary $\partial\Omega$. Under the perturbation of domains keeping those volumes and topological types invariant, we not only refine the proof of its formula for the velocity $G$ but we also develop a new formula for the pressure $R$. Our result may be regarded as the Hadamard variational formula for the Green functions as an example of the elliptic system of equations with the Dirichlet boundary condition.