New approach to the Hadamard variational formula for the Green function of the Stokes equations (Q487157)

The Stokes equations are considered in a two-dimensional bounded domain \(D\). The solution is obtained by using the Green's functions \(G,R\) for velocity and pressure. The variation of \(G,R\) is studied, when \(D\) is perturbed with a preserving volume (and topological type) transformation. The new element is a formula for higher derivatives of \(G,R\) in terms of the domain perturbations, obtained by using also some previous results of the author. The main tools are a Schauder type estimate and some relations concerning the fundamental stress tensor on the surface integrals.