Chinese Quarterly Journal of Mathematics ›› 2009, Vol. 24 ›› Issue (3): 445-452.

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

  

  1. 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);

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

CLC Number: