Differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow

This paper is concerned with the computation of the drag T associated with a body traveling at uniform velocity in a fluid governed by the stationary Navier-Stokes equations. It is assumed that the fluid fills a domain of the form Omega+u, where Omega subset of R(3) is a reference domain and u is a displacement field. We assume only that Omega is a Lipschitz domain and that u is Lipschitz-continuous. We prove that, at least when the velocity of the body is sufficiently small, u-->T(Omega+u) is a C-infinity mapping (in a ball centered at 0). We also compute the derivative at 0.