  Let $\Omega \subset \mathbb{R}^d$ be a bounded open connected set with
Lipschitz boundary. Let $A^N$ and $A^D$ be the Neumann Stokes operator and
Dirichlet Stokes operator on $\Omega$, respectively. Further let $\lambda_1^N
\leq \lambda_2^N \leq \ldots$ and $\lambda_1^D \leq \lambda_2^D \leq \ldots$ be
the eigenvalues of $A^N$ and $A^D$ repeated with multiplicity, respectively.
Then \[ \lambda_{n+1}^N < \lambda_n^D \] for all $n \in \mathbb{N}$.
