In this paper, we prove the existence of a random exponential attractor (a positively invariant, compact, random set with finite fractal dimension that attracts any trajectory exponentially) for the 3D non-autonomous damped Navier–Stokes equation with additive noise, which implies that the asymptotic behavior of solutions for the equation can be described by finite independent parameters. The key and difficult point of this proof lies in proving the Lipschitz continuity and the random squeezing property in mean sense for the non-autonomous random dynamical system generated by solutions of the equation.

中文翻译：

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3D非自治随机阻尼Navier-Stokes方程的随机指数吸引子

在本文中，我们证明了带有加性噪声的3D非自治阻尼Navier-Stokes方程存在一个随机指数吸引子（一个正定不变，紧致，具有有限分数维的随机集，它以指数形式吸引任何轨迹），这表明方程解的渐近行为可以用有限的独立参数来描述。该证明的关键和难点在于证明由方程解产生的非自治随机动力系统的均值意义上的Lipschitz连续性和随机压缩性质。