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

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