HAN Yinghao,SU Hong,YU Jixia.The existence of the invariant measures for 2D stochastic Navier-Stokes-Burgers equation[J].Journal of Yanbian University,2013,39(03):161-166.
随机2-维纳维-斯托克斯-伯格斯方程的不变测度的存在性
- Title:
- The existence of the invariant measures for 2D stochastic Navier-Stokes-Burgers equation
- 文章编号:
- 1004-4353(2013)03-0161-06
- 关键词:
- 随机纳维-斯托克斯-伯格斯方程; 不变测度; 肽紧性
- 分类号:
- O211.63; O175.29
- 文献标志码:
- A
- 摘要:
- 在具有光滑边界的有界区域DR2上,讨论了不可压缩流体的随机2-维纳维-斯托克斯-伯格斯方程du=(Δu+1/2u2+(u·)u)dt+dW(t), 其中W关于时间是白噪声的,关于空间变量是尽可能一般的高斯型时-空随机向量场; 利用Krylov-Bogoliubov判别定理证明了上述方程的不变测度的存在性.
- Abstract:
- We consider the following 2-dimensional Navier-Stokes-Burgers equation for an incompressible fluid in a bounded domain D with smooth boundary du=(Δu+1/2u2+(u·)u)dt+dW(t), where W is a Gaussian form space-time random field, which is white noise in time, and as general as possible in the space variable. The existence of invariant measure for the equation is proved using the Krylov-Bogoliubov theorem.
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备注/Memo
收稿日期: 2013-07-13
作者简介: 韩英豪(1963—),男,理学博士,副教授,研究方向为无穷维动力系统.