Abstract
The long‐time behavior of flows is a very interesting and important problem in the theory of stochastic hydrodynamic equations. Inspired by the theory of dynamic system, we develop a new method to the study of the pathwise exponential behavior of 3D stochastic primitive equations driven by fractional Brownian motion. That is, we show that the weak solutions to the 3D stochastic primitive equations converge exponentially to the unique stationary solution. The result and method presented in this article can be widely applied to the study of long‐time behavior of other hydrodynamic equations with noises including Brownian motion and Lévy noise.
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