We establish resolvent estimates in spaces of bounded solenoidal functions for the Stokes operator in a bounded domain Ω in Rd under the assumptions that Ω is C1 for d≥3
Nearby in the stack
and Lipschitz for
d=2
. As a corollary, it follows that the Stokes operator generates a uniformly bounded analytic semigroup in the spaces of bounded solenoidal functions in
Ω
. The smoothness conditions on
Ω
are sharp. The case of exterior domains with nonsmooth boundaries is also studied.The key step in the proof involves new estimates which connect the pressure to the velocity in the