Random Exponential Attractor for the 3D Non-autonomous Stochastic Damped Navier-Stokes Equation

被引：6
|
作者：
Han, Zongfei [1 ]
Zhou, Shengfan [2 ]
机构：
[1] Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2023年 / 35卷 / 02期
基金：
中国国家自然科学基金;
关键词：
Random exponential attractor; Non-autonomous random dynamical system; Damped Navier– Stokes equation; Additive noise;
D O I：
10.1007/s10884-021-09951-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove the existence of a random exponential attractor (a positively invariant, compact, random set with finite fractal dimension that attracts any trajectory exponentially) for the 3D non-autonomous damped Navier-Stokes equation with additive noise, which implies that the asymptotic behavior of solutions for the equation can be described by finite independent parameters. The key and difficult point of this proof lies in proving the Lipschitz continuity and the random squeezing property in mean sense for the non-autonomous random dynamical system generated by solutions of the equation.
引用
收藏
页码：1133 / 1149
页数：17
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