Navier--Stokes equations on a rapidly rotating sphere

D. Wirosoetisno

doi:10.3934/dcdsb.2015.20.1251

Article Contents

2015, Volume 20, Issue 4: 1251-1259. Doi: 10.3934/dcdsb.2015.20.1251

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Navier--Stokes equations on a rapidly rotating sphere

D. Wirosoetisno^1,

1.
Mathematical Sciences, Durham University, Durham DH1 3LE

Received: March 2014

Revised: October 2014

Published: June 2015

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Abstract

We extend our earlier $\beta$-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 $1/\epsilon$ becomes zonal in the long time limit, in the sense that the non-zonal component of the energy becomes bounded by $\epsilon M$. 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.

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Mathematics Subject Classification: Primary: 35B40, 35B41, 35R01, 76D05.

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References

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