An Existence Theorem¶for the Navier-Stokes Flow¶in the Exterior of a Rotating Obstacle
- Cite this article as:
- Hishida, T. Arch. Rational Mech. Anal. (1999) 150: 307. doi:10.1007/s002050050190
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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 L1/2. 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 L2, where ω stands for the angular velocity of the rotating obstacle and P denotes the projection associated with the Helmholtz decomposition.