带弱阻尼Navier-Stokes方程拉回吸引子的收敛性

数学物理学报 ›› 2022, Vol. 42 ›› Issue (4): 1173-1185.

带弱阻尼Navier-Stokes方程拉回吸引子的收敛性

曹洁¹(),黄兰²(),苏克勤^1,*()

¹ 河南农业大学信息与管理科学学院郑州 450046
² 华北水利水电大学数学与统计学院郑州 450045

收稿日期:2021-10-26 出版日期:2022-08-26 发布日期:2022-08-08
通讯作者: 苏克勤 E-mail:caojie23@hotmail.com;huanglan82@hotmail.com;keqinsu@hotmail.com
作者简介:曹洁, E-mail: caojie23@hotmail.com|黄兰, E-mail: huanglan82@hotmail.com
基金资助:
河南省自然科学基金(212300410164)

The Convergence of Pullback Attractors for Navier-Stokes Equations with Weak Damping

Jie Cao¹(),Lan Huang²(),Keqin Su^1,*()

¹ College of Information and Management Science, Henan Agricultural University, Zhengzhou 450046
² College of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450045

Received:2021-10-26 Online:2022-08-26 Published:2022-08-08
Contact: Keqin Su E-mail:caojie23@hotmail.com;huanglan82@hotmail.com;keqinsu@hotmail.com
Supported by:
the Henan Natural Science Foundation(212300410164)

摘要/Abstract

摘要：

该文研究了带弱阻尼Navier-Stokes方程解的长时间动力学行为. 在外力项及初值的适当假设条件下, 利用Galerkin方法证明了弱解的整体适定性及正则性, 并根据吸引子基本理论验证了拉回吸引子的存在性及收敛性.

关键词: 拉回吸引子, Navier-Stokes方程, 弱阻尼, 上半连续性

Abstract:

The long-time behavior of solution to Navier-Stokes equations with weak damping is studied in this paper. With some assumptions on the external force and initial datum, the global wellposedness and regularity of weak solution are proved by Galerkin method, and the existence and convergence of pullback attractors are established finally.

Key words: Pullback attractors, Navier-Stokes equations, Weak damping, Upper semicontinuity

中图分类号:

O175.26

曹洁,黄兰,苏克勤. 带弱阻尼Navier-Stokes方程拉回吸引子的收敛性[J]. 数学物理学报, 2022, 42(4): 1173-1185.

Jie Cao,Lan Huang,Keqin Su. The Convergence of Pullback Attractors for Navier-Stokes Equations with Weak Damping[J]. Acta mathematica scientia,Series A, 2022, 42(4): 1173-1185.

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