带弱耗散的两维非自治不可压Navier-Stokes方程拉回吸引子的上半连续性

数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 722-739.

带弱耗散的两维非自治不可压Navier-Stokes方程拉回吸引子的上半连续性

杨新光¹, 赵明霞², 侯伟³

1. 河南师范大学数学与信息科学学院河南新乡 453007;
2. 平顶山学院数学与信息科学学院河南平顶山 467000;
3. 河南师范大学附属中学河南新乡 453007

收稿日期:2015-12-16 修回日期:2016-05-13 出版日期:2016-08-26 发布日期:2016-08-26
作者简介:杨新光,yangxinguang@hotmail.com;赵明霞,zhaolaoshi_2010@163.com;侯伟,hw730816@163.com
基金资助:
河南师范大学青年骨干教师基金、河南省教育厅自然科学基金（15A110033）和河南省科技厅科技创新项目（142102210448）资助

Upper Semi-Continuity of Pullback Attractors for the 2D Non-Autonomous Navier-Stokes Equations with Weak Damping

Yang Xinguang¹, Zhao Mingxia², Hou Wei³

1. College of Mathematical and Informational Science, Henan Normal University, Henan Xinxiang 453007;
2. College of Mathematical and Informational Science, Pingdingshan University, Henan Pingdingshan 467000;
3. High School of Henan Normal University, Henan Xinxiang 453007

Received:2015-12-16 Revised:2016-05-13 Online:2016-08-26 Published:2016-08-26
Supported by:
Support by the Mainstay Fund from Henan Normal University,the Foundation of Henan Educational Committee(15A110033) and the Program for Science and Technology Innovation Grant of Henan Province(142102210448)

摘要/Abstract

摘要：

该文研究了描述流体力学规律的一类带有弱耗散和扰动外力项的两维非自治不可压Navier-Stokes方程拉回吸引子的上半连续性. 利用半群（过程族）的分解方法以及弱连续方法，可以得到自治系统全局吸引子和非自治系统拉回吸引子的存在性，进一步地，当ε>0收敛到ε=0时候，非自治系统的拉回吸引子A_ε（t）可以连续收敛到自治系统的全局吸引子A.

关键词: Navier-Stokes方程, 拉回吸引子, 上半连续

Abstract:

In this paper, the upper semi-continuity of pullback attractors for the 2D non-autonomous Navier-Stokes equations with weak damping and external force perturbation terms which describes the motion of fluid with weak damping was considered. By decomposition of process (semigroup) and some estimates, we obtained the pullback attractors A_ε(t) of equation (1.1) with ε>0 converges to the global attractor A of equation (1.1) with ε=0 for any t∈R.

Key words: Navier-Stokes equation, Pullback attractors, Upper semi-continuity

中图分类号:

O175.2

杨新光, 赵明霞, 侯伟. 带弱耗散的两维非自治不可压Navier-Stokes方程拉回吸引子的上半连续性[J]. 数学物理学报, 2016, 36(4): 722-739.

Yang Xinguang, Zhao Mingxia, Hou Wei. Upper Semi-Continuity of Pullback Attractors for the 2D Non-Autonomous Navier-Stokes Equations with Weak Damping[J]. Acta mathematica scientia,Series A, 2016, 36(4): 722-739.

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