, Volume 150, Issue 4, pp 307-348

An Existence Theorem¶for the Navier-Stokes Flow¶in the Exterior of a Rotating Obstacle

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Abstract:

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 L 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 in the space L 2, where ω stands for the angular velocity of the rotating obstacle and P denotes the projection associated with the Helmholtz decomposition.

Accepted: March 26, 1999