Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations

Sun CF; Gao HJ

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Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations

机译：随机Navier-Stokes-Voight方程和本原方程的随机吸引子的Hausdorff维数

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We study the three dimensional stochastic Navier-Stokes-Voight model of viscoelastic incompressible fluid and three dimensional stochastic Primitive Equations with additive noise. In [12] and [11], we showed that, the long time dynamics is captured by a random attractor, along this line, in this paper, we show that the Hausdorff dimension of attractor is an invariant random variable, and it is bounded by d, provided the random dynamics system contracts d-dimensional volumes exponentially fast.

机译：我们研究了粘弹性不可压缩流体的三维随机Navier-Stokes-Voight模型和具有加性噪声的三维随机本原方程。在[12]和[11]中，我们表明，长时间动态是由随机吸引子捕获的，沿着这条线，在本文中，我们表明吸引子的Hausdorff维数是一个不变的随机变量，并且它是有界的如果随机动力学系统以d指数速度快速收缩d维体积，则可以用d表示。

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来源
《Dynamics of partial differential equations》 |2010年第4期|共20页
作者
Sun CF; Gao HJ;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Hausdorff dimension; Navier-Stokes-Voight equations; primitive equations;

机译：Hausdorff维数;Navier-Stokes-Voight方程;本原方程;

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专利

1. Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations [J] . Sun CF, Gao HJ Dynamics of partial differential equations . 2010,第4期

机译：随机Navier-Stokes-Voight方程和本原方程的随机吸引子的Hausdorff维数
2. Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations [J] . Hongjun Gao, Chengfeng Sun Dynamics of partial differential equations . 2010,第4期

机译：随机Navier-Stokes-Voight方程和本原方程的随机吸引子的Hausdorff维数
3. Hausdorff Dimension of a Random Attractor for Stochastic Boussinesq Equations with Double Multiplicative White Noises [J] . Li Yin, Wei Ruiying, Cai Donghong Journal of Function Spaces . 2016,第1期

机译：随机BOUSINESQ方程随机吸引子的Hausdorff尺寸，双倍增白色噪音
4. Random Attractor of the Stochastic Lattice Reversible Selkov Equations with Additive Noises [C] . Hongyan Li The Thirteenth IEEE International Conference on E-Business Engineering . 2016

机译：具有加性噪声的随机格子可逆Selkov方程的随机吸引子
5. Existence of Random Attractors of Stochastic Fractional Reaction-Diffusion Equations in Bounded Domains [D] . ?Attanasio, Ayla Jean 2020

机译：有界畴内随机分数反应扩散方程的随机吸引子存在
6. On stochastic differential equations with arbitrarily slow convergence rates for strong approximation in two space dimensions [O] . Máté Gerencsér, Arnulf Jentzen, Diyora Salimova -1

机译：具有二维空间强逼近的具有任意慢收敛速度的随机微分方程
7. Upper and lower bounds for the Hausdorff dimension of the attractor for reaction-diffusion equations in $mathbb{R}^n$ (Nonlinear Evolution Equations and Applications) [O] . Efendiev Messoud A., Scheel A. 1999

机译：$ mathbb {R} ^ n $中的反应扩散方程吸引子的Hausdorff维数的上限和下限（非线性演化方程和应用）

Hausdorff dimension of random attractor for stochastic Navier-Stokes-Voight equations and primitive equations

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