In this paper, an asymptotic log-Harnack inequality and some consequent properties are established via the asymptotic coupling method for a class of stochastic 2D hydrodynamical-type systems driven by degenerate noise. The main results are applicable to the stochastic 2D Navier–Stokes equations, stochastic 2D magneto-hydrodynamic equations and stochastic 2D Boussinesq equations, stochastic 2D magnetic Bénard problem, stochastic 3D Leray-\(\alpha \) model and also stochastic shell models of turbulence in the degenerate noise case.

中文翻译：

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退化噪声的随机二维流体动力系统的渐近对数-Harnack不等式及应用

本文通过渐近耦合方法，针对一类由简并噪声驱动的随机二维流体动力系统，建立了渐近对数-Harnack不等式和相应的性质。主要结果适用于随机2D Navier–Stokes方程，随机2D磁流体动力学方程和随机2D Boussinesq方程，随机2D磁Bénard问题，随机3D Leray- （（alpha））模型以及随机壳模型在退化的噪声情况下。