Convergence of global attractors of a 2D non-Newtonian system to the global attractor of the 2D Navier-Stokes system  

作　　者：ZHAO CaiDi DUAN JinQiao 

机构地区：[1]Department of Mathematics and Information Science,Wenzhou University [2]Department of Applied Mathematics,Illinois Institute of Technology

出　　处：《Science China Mathematics》2013年第2期253-265,共13页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.10901121,11271290 and 11028102);National Basic Research Program of China(Grant No.2012CB426510);Natural Science Foundation of Zhejiang Province(Grant No.Y6080077);Natural Science Foundation of Wenzhou University(Grant No.2008YYLQ01);Zhejiang Youth Teacher Training Project;Wenzhou 551 Project;the Fundamental Research Funds for the Central Universities(Grant No.2010ZD037)

摘　　要：This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional （2D） incompressible non-Newtonian fluid system and the 2D Navier-Stokes system. We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm. Then we establish that the global attractors {.Aε^H}0〈≤1 of the non-Newtonian fluid system converge to the global attractor .A0H of the Navier-Stokes system as ε → 0. We also construct the minimal limit A^H min of the H global attractors {Aε^H}0〈ε≤ as ≤→ 0 and prove that A^Hmin iS a strictly invariant and connected set.This paper discusses the relation between the long-time dynamics of solutions of the two-dimensional(2D) incompressible non-Newtonian fluid system and the 2D Navier-Stokes system.We first show that the solutions of the non-Newtonian fluid system converge to the solutions of the Navier-Stokes system in the energy norm.Then we establish that the global attractors {AHε} 0<ε≤1 of the non-Newtonian fluid system converge to the global attractor AH0 of the Navier-Stokes system as → 0.We also construct the minimal limit AHmin of the global attractors {AHε}0<ε≤1 as ε→ 0 and prove that AHmin is a strictly invariant and connected set.

关 键 词：non-Newtonian fluid system Navier-Stokes system global attractors infinite dimensional dynamical systems 

分 类 号：O373[理学—流体力学] TS103.63[理学—力学]