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

TL;DR

This paper proves the existence of invariant measures for a stochastic inviscid 3-layer quasi-geostrophic model, demonstrating long-term statistical stability under random forcing in a bounded domain.

Contribution

It establishes well-posedness and invariant measures for the stochastic inviscid multi-layer quasi-geostrophic equations, extending previous methods to this complex fluid model.

Findings

Existence of invariant measures supported on bounded functions.

Well-posedness of the stochastic model under natural regularity assumptions.

Application of Krylov-Bogoliubov approach to this geophysical fluid system.

Abstract

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).