Weak and strong averaging principle for a stochastic coupled fast–slow atmosphere–ocean model with non-Lipschitz Lévy noise. (May 2022)

• Record Type: Journal Article
• Authors: Shi, Yangyang; Gao, Hongjun
• Is Part Of: Nonlinear analysis. Volume 218(2022)
• Publication Date: 2022-05
• Subjects: 37N10 -- 70K65 -- 70K70; Stochastic coupled atmosphere–ocean model -- Lévy noise -- Averaging principle -- Invariant measures; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.112794
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the averaging principle for a stochastic coupled fast–slow atmosphere–ocean model with non-Lipschitz Lévy noise. Precisely, we will first explore the well-posedness of the model. And next, we prove regularity estimates and tightness of the slow variables. Then, we prove the ergodicity of the fast variable with the frozen slow variables. In the end, we prove that the slow variables converge to the solution of the averaged equations in probability and p th-mean ( 1 < p < 2 ), under different conditions, as time scale parameter ɛ goes to zero.