Abstract
In this paper, the authors investigate the probability distribution of solutions within the phase space for the non-autonomous tropical climate model in two-dimensional bounded domains. They first prove that the associated process possesses a pullback attractor and a family of invariant Borel probability measures. Then they establish that this family of invariant Borel probability measures satisfies Liouville’s theorem and is a statistical solution of the tropical climate model. Afterwards, they prove that the statistical solution possesses degenerate Lusin’s type regularity provided that the associated Grashof number is small enough.
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