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Existence of periodic solutions and their asymptotic stability to the Navier–Stokes equations with the Coriolis force

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Abstract

We consider the time-periodic problem for the Navier–Stokes equations in the rotational framework. We prove the unique existence of time-periodic solutions for the prescribed external force. Furthermore, we also show the asymptotic stability of small time-periodic solutions provided the initial disturbance is sufficiently small.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo, 169–8555, Japan

    Hideo Kozono

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

    Yuki Mashiko & Ryo Takada

Authors
  1. Hideo Kozono
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  2. Yuki Mashiko
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  3. Ryo Takada
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Correspondence to Hideo Kozono.

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Kozono, H., Mashiko, Y. & Takada, R. Existence of periodic solutions and their asymptotic stability to the Navier–Stokes equations with the Coriolis force. J. Evol. Equ. 14, 565–601 (2014). https://doi.org/10.1007/s00028-014-0228-4

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