Existence of Invariant Measures for Stochastic Inviscid Multi-Layer Quasi-Geostrophic Equations
- Authors: Federico Butori, Francesco Grotto, Eliseo Luongo, Leonardo Roveri
- Preprint year: 2023
- First public date: 2023-08-22
- arXiv: 2308.11559
- Status: Published
- Publication type: Journal article
- Publication year: 2024
- Published online: 2024-10-23
- Journal: Milan Journal of Mathematics 92(2), 397–425 (2024)
- DOI: 10.1007/s00032-024-00408-6
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).