The Existence of Global Attractors for 2D Navier-Stokes Equations in H^k Spaces  

作　　者：Yin Di ZHANG Ling Yu SONG Tian MA 

机构地区：[1]Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, P. R. China [2]School of Science, Chang'an University, Xi'an 710064, P. R. China [3]Mathematical College, Si'chuan University, Chengdu 610064, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第1期51-58,共8页数学学报（英文版）

基　　金：Supported by the NSF of China (Nos. 10571142, 10771167)

摘　　要：In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.In this paper, we prove that the 2D Navier-Stokes equations possess a global attractor in Hk（Ω,R2） for any k ≥ 1, which attracts any bounded set of Hk（Ω,R2） in the H^k-norm. The result is established by means of an iteration technique and regularity estimates for the linear semigroup of operator, together with a classical existence theorem of global attractor. This extends Ma, Wang and Zhong＇s conclusion.

关 键 词：Navier-Stokes equations semigroup of operator global attractor regularity of attractor 

分 类 号：O152.7[理学—数学]