An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle

We consider the three-dimensional Navier-Stokes initial value problem in the exterior of a rotating obstacle. It is proved that a unique solution exists locally in time if the initial velocity possesses the regularity H-1/2. This regularity assumption is the same as that in the famous paper of FUJITA & KATO. An essential step for the proof is the deduction of a certain smoothing property together with estimates near t = 0 of the semigroup, which is not an analytic one, generated by the operator, Lu = -P [Delta u + (w x x).del u - w x u] in the space L-2, where w stands for the angular velocity of the rotating obstacle and P denotes the projection associated with the Helmholtz decomposition.