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Navier--Stokes equations on a rapidly rotating sphere

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


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