Navier-Stokes equations on the β-plane

2010/09/23 by Mustafa Al-Jaboori, Al-Jaboori, Mustafa, Djoko Wirosoetisno +1
Mathematics · #35B40 #35B41 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35B41 #msc:76D05

paper · pdf · doi:10.48550/arxiv.1009.4538

arxiv created 2010/09/23 · arxiv updated 2010/09/24

Abstract

We show that, given a sufficiently regular forcing, the solution of the two-dimensional Navier--Stokes equations on the periodic β-plane (i.e. with the Coriolis force varying as f0+βy) will become nearly zonal: with the vorticity ω(x,y,t)=\wb(y,t)+\wt(x,y,t), one has |\wt|Hs2≤β-1 Ms(\...) as t→∞. We use this show that, for sufficiently large β, the global attractor of this system reduces to a point.

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