[1]韩英豪,张磊,杨永芳,等.分形布朗运动驱动的Navier-Stokes方程的渐近行为[J].延边大学学报(自然科学版),2015,41(02):95-102.
　HAN Yinghao,ZHANG Lei,YANG Yongfang,et al.The asymptotic behavior of the Navier-Stokes equation driven by fractional Brownian motion[J].Journal of Yanbian University,2015,41(02):95-102.
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分形布朗运动驱动的Navier-Stokes方程的渐近行为

《延边大学学报(自然科学版)》[ISSN:1004-4353/CN:22-1191/N] 卷: 第41卷 期数: 2015年02期 页码: 95-102 栏目: 基础科学研究 出版日期: 2015-05-30
Title:
The asymptotic behavior of the Navier-Stokes equation driven by fractional Brownian motion
作者:
韩英豪; 张磊; 杨永芳; 胡晓雪
辽宁师范大学 数学学院, 辽宁 大连 116029
Author(s):
HAN Yinghao;  ZHANG Lei;  YANG Yongfang;  HU Xiaoxue
School of Mathematics, Liaoning Normal University, Dalian 116029, China
关键词:
分形布朗运动;  随机拉回吸引子;  Navier-Stokes方程
Keywords:
fractional Brownian motion;  random pullback attraction;  Navier-Stokes equation
分类号:
O211.63; O175.29
文献标志码:
A
摘要:
在具有光滑边界O的有界区域O∈R2上考虑了如下由Hurst参数为h∈(1/2,1)的分形布朗运动驱动的非自治Navier-Stokes方程的长时间动力行为(du)/(dt)+(u·)u-υΔu+p=f(x,t)+(dBh(t))/(dt).在适当的条件下,应用先验估计方法证明了由上述方程生成的随机动力系统的随机吸引子的存在性.
Abstract:
On a bounded domain O∈R2 with a smooth boundary O, we consider the long time dynamic behavior of the following non-autonomous Navier-Stokes equation driven by fractional Brownian motion with Hurst parameter h∈(1/2,1):(du)/(dt)+(u·)u-υΔu+p=f(x,t)+(dBh(t))/(dt). Under suitable condition, we use the uniform estimates method to prove the existence of the random pullback attractor for the random dynamical system generated by above equation.

参考文献/References:

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备注/Memo

收稿日期: 2015-05-28 基金项目: 国家自然科学基金资助项目(61304056)通信作者: 韩英豪(1963—),男,理学博士,副教授,研究方向为无穷维动力系统.

更新日期/Last Update: 2015-05-30