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Asymptotic limit of fast rotation for the incompressible Navier–Stokes equations in a 3D layer

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Abstract

We consider the initial value problem for the Navier–Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling-invariant space when the speed of rotation is sufficiently high. Furthermore, we consider the asymptotic limit of the fast rotation and show that the global solution converges to that of 2D incompressible Navier–Stokes equations in some global in time space-time norms.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Numbers JP19K03584, JP18KK0072, JP17H02851 and JP20H01814.

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  1. Faculty of Mathematics, Kyushu University, Fukuoka, 819–0395, Japan

    Hiroki Ohyama & Ryo Takada

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  1. Hiroki Ohyama
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  2. Ryo Takada
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Correspondence to Hiroki Ohyama.

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Ohyama, H., Takada, R. Asymptotic limit of fast rotation for the incompressible Navier–Stokes equations in a 3D layer. J. Evol. Equ. 21, 2591–2629 (2021). https://doi.org/10.1007/s00028-021-00697-z

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