  We show that the eigenvalues of the Stokes operator in a domain with a small
hole converge to the eigenvalues of the Stokes operator in the whole domain,
when the diameter of the hole tends to 0. The convergence of the eigenspaces
and the convergence of the Stokes semigroup are also established. Concerning
the Navier--Stokes equations, we prove that the vorticity of the solution in
the perforated domain converges as the hole shrinks to a point $r$ to the
vorticity of the solution in the punctured domain (i.e. the whole domain with
the point $r$ removed). The main ingredients of the analysis are a suitable
decomposition of the vorticity space, the formalism elaborated in [7] and some
basics of potential theory.
