Archive for Rational Mechanics and Analysis

, Volume 150, Issue 4, pp 307–348

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

  • Toshiaki Hishida

DOI: 10.1007/s002050050190

Cite this article as:
Hishida, T. Arch. Rational Mech. Anal. (1999) 150: 307. doi:10.1007/s002050050190


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.

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Toshiaki Hishida
    • 1
  1. 1.Department of Applied Mathematics¶Faculty of Engineering¶Niigata University¶Niigata 950-2181 JapanJP