Let (SDΩ) be the Stokes operator defined in a bounded domain Ω of R with Dirichlet boundary conditions. We first prove that, generically with respect to the domain Ω, all the eigenvalues of (SDΩ) are simple. That answers positively a question raised by J. H. Ortega and E. Zuazua in [18, Section 6]. Our second result states that, generically with respect to… (More)