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Archive for Rational Mechanics and Analysis

, Volume 213, Issue 2, pp 689–703 | Cite as

Periodic Motions of Stokes and Navier–Stokes Flows Around a Rotating Obstacle

  • Thieu Huy NguyenEmail author
Article

Abstract

We prove the existence and uniqueness of periodic motions to Stokes and Navier–Stokes flows around a rotating obstacle \({D \subset \mathbb{R}^3}\) with the complement \({\Omega = \mathbb{R}^3 \backslash D}\) being an exterior domain. In our strategy, we show the C b -regularity in time for the mild solutions to linearized equations in the Lorentz space \({L^{3,\infty}(\Omega)}\) (known as weak-L 3 spaces) and prove a Massera-typed Theorem on the existence and uniqueness of periodic mild solutions to the linearized equations in weak-L 3 spaces. We then use the obtained results for such equations and the fixed point argument to prove such results for Navier–Stokes equations around a rotating obstacle. We also show the stability of such periodic solutions.

Keywords

Periodic Solution Periodic Motion Mild Solution Lorentz Space Stokes Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHanoiVietnam
  2. 2.Arbeitsgruppe Angewandte Analysis, Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany

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