Exponential Mixing for 3D Stochastic Primitive Equations

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.