Long-time behavior of 3D Stochastic Planetary Geostrophic Viscous Model

TL;DR

This paper demonstrates that the 3D stochastic planetary geostrophic viscous model exhibits exponential ergodicity and possesses a finite-dimensional global attractor when driven by additive noise, linking stochastic dynamics with long-term behavior.

Contribution

It establishes the exponential ergodicity and existence of a finite-dimensional global attractor for the 3D stochastic planetary geostrophic viscous model, a novel result in this context.

Findings

Model has exponential ergodicity.

Global attractor has finite Hausdorff dimension.

Support of invariant measure equals the minimal global attractor.

Abstract

This paper reports the 3D planetary geostrophic viscous model has the exponential ergodicity and global attractor if this model is driven by an additive random noise, which results in the support of the integration of invariant measure for the dynamic is exactly a minimal global attractor. It's worth mentioning that this global attractor has finite Hausdorff dimension.