Exponential Mixing for 3D Stochastic Primitive Equations

2015/06/29 by Zhao Dong, Dong, Zhao, Jianliang Zhai +3
Computer Science · Economics, Econometrics and Finance · Engineering · #60H30 60H15 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1506.08514

openalex publication_date 2015/06/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that weak solutions of 3D stochastic primitive equations have exponential mixing property if the noise is sufficiently smooth and non-degenerate. With the help of uniqueness of strong solution of 3D stochastic primitive equations, we obtain that all weak solutions which are limitations of Galerkin approximations share the same invariant measure. In particular, the invariant measure of strong solution is unique. The coupling method plays a key role.

Citations

• On the equations of the large-scale ocean

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