Consider the Stokes semigrou T-infinity defined on L-sigma(infinity) (Omega) where Omega subset of R-n, n >= 3, denotes an exterior domain with smooth boundary. It is shown that T-infinity(z)u(0) for u(0) is an element of L-sigma(infinity) (Omega) and z is an element of Sigma(theta) with theta is an element of (0, pi/2) satisfies pointwise estimates similar to the ones known for G(z)u(0) where G denotes the Gaussian semigroup on R-n. In particular, T-infinity extends to a bounded analytic semigroup on L-sigma(infinity) (Omega) of angle pi/2. Moreover, T-infinity (t) allows L-sigma(infinity)(Omega) - C2+alpha((Omega) over bar) smoothing for every t > 0 and the Stokes semigroups T-p and T-q on L-sigma(p) (Omega) and L-sigma(q) (Omega) are consistent for all p, q is an element of (1, infinity]. (C) 2014 Elsevier Inc. All rights reserved.
