Almost-sure exponential mixing of passive scalars by the stochastic Navier–Stokes equations
Almost-sure exponential mixing of passive scalars by the stochastic Navier–Stokes equations
复制标题
随机纳维-斯托克斯方程几乎肯定的无源标量指数混合
作者：
J. Bedrossian;A. Blumenthal;Samuel Punshon
我们推导出几乎必然的指数快速混合的被动标量平流随机强迫的二维Navier-Stokes方程和三维超粘性Navier-Stokes方程的解在$\mathbb T^d$受到非denegenerate $H^\sigma$-正则噪声的任何$\sigma$足够大。也就是说，对于所有s > 0，都有一个确定的指数衰减率，使得所有均值为零的H^s被动标量都以相同的速率以概率1在H^{-s}中衰减。这相当于动力系统文献中拉格朗日流的\n {猝灭相关衰减}。这是我们之前工作的后续，它为拉格朗日流建立了一个正的李雅普诺夫指数-一般来说，几乎肯定的指数混合比这强得多。我们的方法也适用于根据有限维流体模型，例如Galerkin截断的Navier-Stokes或Stokes方程非常退化强迫的速度场的演变。对于所有0\leq k < \infty $，我们展示了许多C^k_t C^\infty_x$随机速度场的例子，它们几乎是指数快速混合器。
We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of the stochastically-forced 2D Navier-Stokes equations and 3D hyper-viscous Navier-Stokes equations in $\mathbb T^d$ subjected to non-denegenerate $H^\sigma$-regular noise for any $\sigma$ sufficiently large. That is, for all $s > 0$ there is a deterministic exponential decay rate such that all mean-zero $H^s$ passive scalars decay in $H^{-s}$ at this same rate with probability one. This is equivalent to what is known as \emph{quenched correlation decay} for the Lagrangian flow in the dynamical systems literature. This is a follow-up to our previous work, which establishes a positive Lyapunov exponent for the Lagrangian flow-- in general, almost-sure exponential mixing is much stronger than this. Our methods also apply to velocity fields evolving according to finite-dimensional fluid models, for example Galerkin truncations of Navier-Stokes or the Stokes equations with very degenerate forcing. For all $0 \leq k < \infty $ we exhibit many examples of $C^k_t C^\infty_x$ random velocity fields that are almost-sure exponentially fast mixers.
登录
查看更多内容
影响因子：
3
作者：
J. Bedrossian;A. Blumenthal;Samuel Punshon-Smith
通讯作者：
J. Bedrossian;A. Blumenthal;Samuel Punshon-Smith
影响因子：
2
作者：
Bedrossian, Jacob;Blumenthal, Alex;Punshon-Smith, Sam
通讯作者：
Punshon-Smith, Sam
各种尺寸的通用搅拌机
影响因子：
1.7
作者：
Elgindi, Tarek M.;Zlatoš, Andrej
通讯作者：
Zlatoš, Andrej
无限维控制问题中的标度和饱和及其在随机偏微分方程中的应用
影响因子：
2.8
作者：
Glatt-Holtz, Nathan E.;Herzog, David P.;Mattingly, Jonathan C.
通讯作者：
Mattingly, Jonathan C.
随机流体力学中的拉格朗日混沌和标量平流
影响因子：
2.6
作者：
Bedrossian, Jacob;Blumenthal, Alex;Punshon-Smith, Sam
通讯作者：
Punshon-Smith, Sam