数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (6): 1590-1608.doi: 10.1016/S0252-9602(16)30092-3

• 论文 • 上一篇    下一篇

LARGE TIME BEHAVIOR OF A THIRD GRADE FLUID SYSTEM

柴晓娟, 陈正争, 钮维生   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, China
  • 收稿日期:2015-08-08 修回日期:2016-05-02 出版日期:2016-12-25 发布日期:2016-12-25
  • 通讯作者: Weisheng NIU,E-mail:niuwsh@ahu.edu.cn E-mail:niuwsh@ahu.edu.cn
  • 作者简介:Xiaojuan CHAI,E-mail:chaixj@ahu.edu.cn;Zhengzheng CHEN,E-mail:chenzz@ahu.edu.cn
  • 基金资助:

    Supported by NSFC (11301003, 11426031, 11501560), the Research Fund for Doctor Station of the Education Ministry of China (20123401120005), NSF of Anhui Province (1308085QA02).

LARGE TIME BEHAVIOR OF A THIRD GRADE FLUID SYSTEM

Xiaojuan CHAI, Zhengzheng CHEN, Weisheng NIU   

  1. School of Mathematical Sciences, Anhui University, Hefei 230601, China
  • Received:2015-08-08 Revised:2016-05-02 Online:2016-12-25 Published:2016-12-25
  • Contact: Weisheng NIU,E-mail:niuwsh@ahu.edu.cn E-mail:niuwsh@ahu.edu.cn
  • Supported by:

    Supported by NSFC (11301003, 11426031, 11501560), the Research Fund for Doctor Station of the Education Ministry of China (20123401120005), NSF of Anhui Province (1308085QA02).

摘要:

We consider the large time behavior of a non-autonomous third grade fluid system, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem admits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.

关键词: third grade fluid equations, uniform attractor, upper-semicontinuity

Abstract:

We consider the large time behavior of a non-autonomous third grade fluid system, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem admits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.

Key words: third grade fluid equations, uniform attractor, upper-semicontinuity

中图分类号: 

  • 37L30