Existence of Invariant Measures for Stochastic Inviscid Multi-Layer Quasi-Geostrophic Equations

Roveri Leonardo, Università di Pisa
Butori Federico, Scuola Normale Superiore
Grotto Francesco, Università di Pisa
Luongo Eliseo, Scuola Normale Superiore

We consider an inviscid 3-layer quasi-geostrophic model with stochastic forcing 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).

Area: CS4 - Kolmogorov equations and long time behaviour for SPDEs (Carlo Orrieri & Luca Scarpa)

Keywords: Invariant Measure, Quasi-geostrophic, Fluid dynamics, SPDEs, Geophysics

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