  Let (SD_\Omega) be the Stokes operator defined in a bounded domain \Omega of
R^3 with Dirichlet boundary conditions. We prove that, generically with respect
to the domain \Omega with C^5 boundary, the spectrum of (SD_\Omega) satisfies a
non resonant property introduced by C. Foias and J. C. Saut to linearize the
Navier-Stokes system in a bounded domain \Omega of R^3 with Dirichlet boundary
conditions. For that purpose, we first prove that, generically with respect to
the domain \Omega with C^5 boundary, all the eigenvalues of (SD_\Omega) are
simple. That answers positively a question raised by J. H. Ortega and E.
Zuazua. The proofs of these results follow a standard strategy based on a
contradiction argument requiring shape differentiation. One needs to shape
differentiate at least twice the initial problem in the direction of carefully
chosen domain variations. The main step of the contradiction argument amounts
to study the evaluation of Dirichlet-to-Neumann operators associated to these
domain variations.
