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Consider the equations of Navier-Stokes in the exterior of a rotating domain. It is shown that, after rewriting the problem on a fixed domain Ω, the solution of the corresponding Stokes equation is governed by a C0-semigroup on Lσp(Ω), 1 < p < ∞, with generator . Moreover, for and initial data u0 ∈ Lσp(Ω), we prove the existence of a unique local mild solution to the Navier-Stokes problem.

Abstract.: In this paper we show that the parabolic problem associated with elliptic operators A having coefficients in has the property of maximal -regularity.