  The goal of this paper is to investigate the minimisation of the first
eigenvalue of the (vectorial) incompressible Dirichlet-Stokes operator. After
providing an existence result, we investigate optimality conditions and we
prove the following surprising result: while the ball satisfies first and
second-order optimality conditions in dimension 2, it does not in dimension 3,
so that the Faber-Krahn inequality for the Stokes operator is probably true in
$\mathbb{R}^2$, but does not hold in $\mathbb{R}^3$. The multiplicity of the
first eigenvalue of the Dirichlet-Stokes operator in the ball in $\mathbb{R}^3$
plays a crucial role in the proof of that claim.
