Abstract
The objection of this paper is to study the asymptotical behavior of solutions for the three dimensional planetary geostrophic equations of large-scale ocean circulation with small additive noise. In this paper, we prove the existence of random attractors for the three dimensional planetary geostrophic equations of large-scale ocean circulation with small additive noise. Furthermore, we prove the random attractor of the three dimensional planetary geostrophic equations of large-scale ocean circulation with small additive noise will be close to the global attractor of the three dimensional planetary geostrophic equations of large-scale ocean circulation for any when the parameter of the perturbation goes to zero.
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