Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (5): 1416-1430.

• Articles • Previous Articles     Next Articles

H1-uniform Attractor for 2D Navier-Stokes Equations

 ZHAO Cai-De   

  1. Department of Mathematics and Information Science, Wenzhou University, Zhejiang Wenzhou 325035
  • Received:2009-10-27 Revised:2010-09-21 Online:2011-10-25 Published:2011-10-25
  • Supported by:

    国家自然科学基金(10901121, 10826091, 10771139)、浙江省自然科学基金 (Y6080077)、中国博士后科学基金(20090460952)、温州大学预研基金(2008YYLQ01)和浙江省高校优秀青年教师及温州市551人才工程资助

Abstract:

This paper is concerned with the existence of uniform attractor and asymptotic smoothing effect of solutions for two-dimensional (2D) nonautonomous Navier-Stokes equations in 2D domains (bounded or not). The author uses the enstrophy equation to obtain the asymptotic compactness of the family of processes associated with the Navier-Stokes equations and establishes the existence of H1-uniform attractor and thus reveal the asymptotic smoothing effect of the solutions in the sense that the solutions become eventually more
regular than the initial data.

Key words: Uniform attractor, Nonautonomous Navier-Stokes equations, Asymptotic smoothing effect

CLC Number: 

  • 35B40
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