论文标题
2D随机Navier-Stokes方程的不变度的大偏差原理与噪声相关性消失
Large deviations principle for the invariant measures of the 2D stochastic Navier-Stokes equations with vanishing noise correlation
论文作者
论文摘要
我们研究了圆环上的二维不可压缩的纳维尔 - 斯托克斯方程，该方程是由高斯噪声驱动的，该噪声是白色的，在太空中是彩色的。我们考虑到随机强迫$ \ sqrt {\ e} $的大小及其相关刻度$δ（\ e）$都很小的情况。我们证明了解决方案以及不变措施家族的巨大偏差原则，因为$ \ e $和$δ（\ e）$同时在适当的缩放下将其发送至$ 0 $。
We study the two-dimensional incompressible Navier-Stokes equation on the torus, driven by Gaussian noise that is white in time and colored in space. We consider the case where the magnitude of the random forcing $\sqrt{\e}$ and its correlation scale $δ(\e)$ are both small. We prove a large deviations principle for the solutions, as well as for the family of invariant measures, as $\e$ and $δ(\e)$ are simultaneously sent to $0$, under a suitable scaling.
