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Navier-Stokes equations on a rapidly rotating sphere

Wirosoetisno, D

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Abstract

We extend our earlier β-plane results [al-Jaboori and Wirosoetisno, 2011, DCDS-B 16:687--701] to a rotating sphere. Specifically, we show that the solution of the Navier--Stokes equations on a sphere rotating with angular velocity 1/ϵ becomes zonal in the long time limit, in the sense that the non-zonal component of the energy becomes bounded by ϵM. Central to our proof is controlling the behaviour of the nonlinear term near resonances. We also show that the global attractor reduces to a single stable steady state when the rotation is fast enough.

Citation

Wirosoetisno, D. (2015). Navier-Stokes equations on a rapidly rotating sphere. Discrete and Continuous Dynamical Systems - Series B, 20(4), 1251-1259. https://doi.org/10.3934/dcdsb.2015.20.1251

Journal Article Type Article
Acceptance Date Jan 15, 2015
Online Publication Date Feb 1, 2015
Publication Date Feb 1, 2015
Deposit Date Sep 29, 2016
Publicly Available Date Sep 13, 2017
Journal Discrete and Continuous Dynamical Systems - Series B
Print ISSN 1531-3492
Electronic ISSN 1553-524X
Publisher American Institute of Mathematical Sciences (AIMS)
Peer Reviewed Peer Reviewed
Volume 20
Issue 4
Pages 1251-1259
DOI https://doi.org/10.3934/dcdsb.2015.20.1251

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Copyright Statement
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and continuous dynamical systems : series B following peer review. The definitive publisher-authenticated version Wirosoetisno, D (2015). Navier-Stokes equations on a rapidly rotating sphere. Discrete and Continuous Dynamical Systems - Series B 20(4): 1251-1259 is available online at: https://doi.org/10.3934/dcdsb.2015.20.1251





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