Existence of Invariant Measures for Stochastic Inviscid Multi-Layer Quasi-Geostrophic Equations
摘要
We consider an inviscid 3-layer quasi-geostrophic model with stochastic forcing and damping in a 2D bounded domain. After establishing well-posedness of such system under natural regularity assumptions on the initial condition and the (additive) noise, we prove the existence of an invariant measure supported on bounded functions by means of the Krylov-Bogoliubov approach developed by Ferrario and Bessaih (Comm. Math. Phys. 377, 2020).