Random attractors for the three dimensional stochastical planetary geostrophic equations of large-scale ocean circulation

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.

Keywords:

• Random attractor
• planetary geostrophic equations
• pullback flattening property
• upper semi-continuity

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Science Foundation of China [Grant number 11401459] and the Natural Science Foundation of Shaanxi Province [Grant number 2015JM1010].