  The abstract theory of critical spaces developed in [22] and [20] is applied
to the Navier-Stokes equations in bounded domains with Navier boundary
conditions as well as no-slip conditions. Our approach unifies, simplifies and
extends existing work in the $L_p$-$L_q$ setting, considerably. As an essential
step, it is shown that the strong and weak Stokes operators with Navier
conditions admit an $\mathcal{H}^\infty$-calculus with
$\mathcal{H}^\infty$-angle 0, and the real and complex interpolation spaces of
these operators are identified.
