二维全平面上具线性阻尼Navier-Stokes方程组的整体吸引子和渐近光滑效应

数学季刊 ›› 2009, Vol. 24 ›› Issue (3): 445-452.

二维全平面上具线性阻尼Navier-Stokes方程组的整体吸引子和渐近光滑效应

1. Department of Mathematics and Information Science, Wenzhou University2. Department of Mathematical Sciences, South China University of Technology3. Department of Applied Mathematics, Shanghai Normal University

收稿日期:2005-12-29 出版日期:2009-09-30 发布日期:2023-06-30
作者简介:ZHAO Cai-di(1977- ), male, native of Yangxin, Hubei, a lecturer of Wenzhou University, Ph.D., engages in partial differential equation and infinite dimensional dynamical systems; LI Yong-sheng (1965- ), male, native of Nanzhang, Hubei, a professor of South China University of Technology, Ph.D., engages in partial differential equation and infinite dimensional dynamical systems; ZHOU Sheng-fan(1963- ), male, native of Guilin, Guangxi, a professor of Shangshai Normal University, Ph.D., engages in dynamical systems and differential equations.
基金资助:
Supported by Natural Science Foundation of China(10771074； 10771139)； Supported by the NSF of Wenzhou University(2007L024)； Supported by the NSF of Zhejiang Province(Y6080077)；

Global Attractors and Asymptotic Smoothing Effect for Navier-Stokes Equations with Linear Damping on R²

1. Department of Mathematics and Information Science, Wenzhou University2. Department of Mathematical Sciences, South China University of Technology3. Department of Applied Mathematics, Shanghai Normal University

Received:2005-12-29 Online:2009-09-30 Published:2023-06-30
About author:ZHAO Cai-di(1977- ), male, native of Yangxin, Hubei, a lecturer of Wenzhou University, Ph.D., engages in partial differential equation and infinite dimensional dynamical systems; LI Yong-sheng (1965- ), male, native of Nanzhang, Hubei, a professor of South China University of Technology, Ph.D., engages in partial differential equation and infinite dimensional dynamical systems; ZHOU Sheng-fan(1963- ), male, native of Guilin, Guangxi, a professor of Shangshai Normal University, Ph.D., engages in dynamical systems and differential equations.
Supported by:
Supported by Natural Science Foundation of China(10771074； 10771139)； Supported by the NSF of Wenzhou University(2007L024)； Supported by the NSF of Zhejiang Province(Y6080077)；

摘要/Abstract

摘要： This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R². The authors prove the existence of L²-global attractor and H¹-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.

关键词: Navier-Stokes equations, global attractor, asymptotic smoothing effect, linear
damping

Abstract: This paper studies the long time behavior of solutions to the Navier-Stokes equations with linear damping on R². The authors prove the existence of L²-global attractor and H¹-global attractor by showing that the corresponding semigroup is asymptotically compact. Thereafter, they establish that the two attractors are the same and thus reveal the asymptotic smoothing effect of the solutions.

Key words: Navier-Stokes equations, global attractor, asymptotic smoothing effect, linear
damping

中图分类号:

O175.2

赵才地, 李用声, 周盛凡. 二维全平面上具线性阻尼Navier-Stokes方程组的整体吸引子和渐近光滑效应[J]. 数学季刊, 2009, 24(3): 445-452.

ZHAO Cai-di, LI Yong-sheng, ZHOU Sheng-fan. Global Attractors and Asymptotic Smoothing Effect for Navier-Stokes Equations with Linear Damping on R² [J]. Chinese Quarterly Journal of Mathematics, 2009, 24(3): 445-452.

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