The exponential behavior of the stochastic three-dimensional primitive equations with multiplicative noise

In this article, we study the stability of weak solutions to the stochastic three-dimensional (3D) primitive equations (PEs) with multiplicative noise. In particular, we prove that under some conditions on the forcing terms, the weak solutions converge exponentially in the mean square and almost surely exponentially to the stationary solutions. We also prove a result related to the stabilization of these equations.