标题： 二维随机纳维-斯托克斯方程的统计估计 显示英文标题

标题： Statistical Estimates for 2D stochastic Navier-Stokes Equations

摘要： 均匀、各向同性、二维随机湍流的统计特征被讨论。 我们推导了由多种随机驱动力维持的二维流动中，体能量耗散率$\mathbb{E} [\varepsilon ]$和涡量耗散率$\mathbb{E} [\chi] $的均值的一些严格界限。 我们表明，在无粘极限下$$\mathbb{E} [ \varepsilon ] \rightarrow 0 \hspace{0.5cm}\mbox{and} \hspace{0.5cm} \mathbb{E} [ \chi ] \lesssim \mathcal{O}(1)$$与二维湍流中的双级联一致。 显示英文摘要

摘要： The statistical features of homogeneous, isotropic, two-dimensional stochastic turbulence are discussed. We derive some rigorous bounds for the mean value of the bulk energy dissipation rate $\mathbb{E} [\varepsilon ]$ and enstrophy dissipation rates $\mathbb{E} [\chi] $ for 2D flows sustained by a variety of stochastic driving forces. We show that $$\mathbb{E} [ \varepsilon ] \rightarrow 0 \hspace{0.5cm}\mbox{and} \hspace{0.5cm} \mathbb{E} [ \chi ] \lesssim \mathcal{O}(1)$$ in the inviscid limit, consistent with the dual-cascade in 2D turbulence.