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Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations

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Book cover Recent Developments of Mathematical Fluid Mechanics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

We consider the stability problem of time periodic solutions for the rotating Navier-Stokes equations. For the non-rotating case, it is known that time periodic solutions to the original Navier-Stokes equations are asymptotically stable under the smallness assumptions both on the time periodic solutions and on the initial disturbances. We shall treat the high-rotating cases, and prove the asymptotic stability of large time periodic solutions for large initial perturbations.

Dedicated to Professor Yoshihiro Shibata on his sixtieth birthday

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Acknowledgements

T. Iwabuchi is partially supported by JSPS Grant-in-Aid for Young Scientists (B) #25800069.

A. Mahalov is partially supported by NSF DMS grant 1419593.

R. Takada was partially supported by JSPS Grant-in-Aid for Research Activity Start-up #25887005.

Author information

Authors and Affiliations

  1. Department of Mathematics, Osaka City University and OCAMI, Sumiyoshi-ku, Osaka, 558-8585, Japan

    Tsukasa Iwabuchi

  2. School of Mathematical and Statistical Science, Arizona State University, 871804, Tempe, AZ, 85287, USA

    Alex Mahalov

  3. Mathematical Institute, Tohoku University, Sendai, 980–8578, Japan

    Ryo Takada

Authors
  1. Tsukasa Iwabuchi
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  2. Alex Mahalov
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  3. Ryo Takada
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Corresponding author

Correspondence to Ryo Takada .

Editor information

Editors and Affiliations

  1. Universität of Zürich, Institut für Mathematik, Zürich, Switzerland

    Herbert Amann

  2. University of Tokyo, Graduate School of Mathematical Sciences, Tokyo, Japan

    Yoshikazu Giga

  3. Department of Mathematics, Waseda University, Tokyo, Japan

    Hideo Kozono

  4. Research Institute for Mathematical Sciences, Kyoto University Kitashirakawa, Kyoto, Japan

    Hisashi Okamoto

  5. Department of Mathematics, Waseda University, Tokyo, Japan

    Masao Yamazaki

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Iwabuchi, T., Mahalov, A., Takada, R. (2016). Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations. In: Amann, H., Giga, Y., Kozono, H., Okamoto, H., Yamazaki, M. (eds) Recent Developments of Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0939-9_17

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