Pullback attractors for three dimensional non-autonomous planetary geostrophic viscous equations of large-scale ocean circulation

Bo You; Chengkui Zhong; Fang Li

doi:10.3934/dcdsb.2014.19.1213

Article Contents

2014, Volume 19, Issue 4: 1213-1226. Doi: 10.3934/dcdsb.2014.19.1213

This issue Previous Article Stochastic averaging principle for dynamical systems with fractional Brownian motion Next Article

Pullback attractors for three dimensional non-autonomous planetary geostrophic viscous equations of large-scale ocean circulation

1.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an,710049
2.
Department of Mathematics, Nanjing University, Nanjing 210093
3.
Department of Mathematics, Nanjing University, Nanjing, 210093

Received: May 31, 2013

Revised: December 31, 2013

Published: May 2014

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Abstract

This paper is devoted to the existence of pullback attractors for the process $\{U(t,\tau)\}_{t\geq \tau}$ associated with the three dimensional non-autonomous planetary geostrophic viscous equations of large-scale ocean circulation. We first prove the existence of pullback absorbing sets in $H$ and $V$ for the process $\{U(t,\tau)\}_{t\geq \tau}$ associated with (1)-(8), and then we prove the existence of a pullback attractor in $H$ by the Sobolev compactness embedding theorem. Finally, we obtain the existence of a pullback attractor in $V$ for the process $\{U(t,\tau)\}_{t\geq \tau}$ associated with (1)-(8) by verifying the pullback $\mathcal{D}$ condition $(PDC)$.

Keywords:

Pullback attractor,
planetary geostrophic viscous equations,
Sobolev compactness embedding theory,
pullback $\mathcal{D}$ condition $(PDC)$.

Mathematics Subject Classification: Primary: 37B55; Secondary: 35Q86.

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