数学物理学报 ›› 2009, Vol. 29 ›› Issue (4): 873-881.

• 论文 • 上一篇    下一篇

无界区域上具线性阻尼的二维 Navier-Stokes 方程的拉回吸引子

  

  1. (1. 四川大学 数学学院|成都 610064, 2. 四川师范大学 数学与软件科学学院, 成都 610066)
  • 收稿日期:2008-01-08 修回日期:2009-02-23 出版日期:2009-08-25 发布日期:2009-08-25
  • 基金资助:

    国家自然科学基金(10371083)资助

Pullback Attractors for Non-autonomous 2D Navier-Stokes Equations with Linear Dampness in Some Unbounded Domains

  1. (1. Department of Mathematics, Sichuan University, Chengdu 610064, 2. Department of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066)
  • Received:2008-01-08 Revised:2009-02-23 Online:2009-08-25 Published:2009-08-25
  • Supported by:

    国家自然科学基金(10371083)资助

摘要:

该文首先介绍拉回渐近紧非自治动力系统的概念, 给出非自治动力系统拉回吸引子存在定理. 最后证明了无界区域上具线性阻尼的二维Navier-Stokes 方程的拉回吸引子的存在性, 并给出了其Fractal维数估计.

关键词: 渐近紧, 过程, 非自治, 线性阻尼, 拉回吸引子

Abstract:

In this paper,  the concept of pullback asymptotically compact non-autonomous dynamical system is firstly introduced. Then, a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system is given. Finally, the existence of a pullback attractor for a non-autonomous 2D Navier-Stokes equation with linear dampness in some unbounded domains is proved. Moreover, the upper bounds of  Fractal dimension of the pullback attractor is estimated.

Key words: Asymptotic compactness, Process, Non-autonomous, Linear dampness, Pullback attractor

中图分类号: 

  • 35B41