Asymptotic behavior of 3-D stochastic primitive equations of large-scale moist atmosphere with additive noise

TL;DR

This paper establishes the existence of a random attractor and invariant measure for 3-D stochastic primitive equations modeling large-scale moist atmosphere, using a novel method that extends deterministic results to stochastic settings.

Contribution

Introduces a new method to prove the existence of random attractors and invariant measures for 3-D stochastic primitive equations on manifolds, advancing stochastic climate modeling.

Findings

Proves existence of a random attractor for the stochastic primitive equations.

Establishes the existence of an invariant measure for the system.

Improves upon previous deterministic attractor results by incorporating stochastic effects.

Abstract

Using a new and general method, we prove the existence of random attractor for the three dimensional stochastic primitive equations defined on a manifold $\D\subset\R^3$ improving the existence of weak attractor for the deterministic model. Furthermore, we show the existence of the invariant measure.