Exponential Mixing for 3D Stochastic Primitive Equations

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.

arXiv admin note: text overlap with arXiv:math/0512056 by other authors

References in corpus (2)

• Local and Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity
• Existence and Regularity of Invariant Measures for the Three Dimensional Stochastic Primitive Equations

Cited by in corpus (4)

• On the small time asymptotics of 3D stochastic primitive equations
• Markov Selection and $W$-strong Feller for 3D Stochastic Primitive Equations
• Asymptotic behavior of 3-D stochastic primitive equations of large-scale moist atmosphere with additive noise
• A moderate deviation principle for 2D stochastic primitive equations