The current paper is devoted to the stochastic tamed 3D Naiver-Stokes equation with degenerate noise with degenerate random forcing. We prove that the associated Markov semigroup possesses an exponentially attracting invariant measure by showing that the corresponding dynamical system possesses a strong type of Lyapunov structure along with a special type of gradient inequality and is of a relatively weak form of irreducibility.

中文翻译：

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具有退化噪声的随机驯服3D Navier-Stokes方程的指数混合特性

本文致力于具有退化噪声和退化随机强迫的随机驯服的3D Naiver-Stokes方程。通过证明相应的动力学系统具有强类型的Lyapunov结构以及特殊类型的梯度不等式，并且具有相对弱的不可约形式，我们证明了相关的Markov半群具有指数吸引不变测度。