Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418084 | Journal of Mathematical Analysis and Applications | 2015 | 15 Pages |
Abstract
This paper is concerned with the three-dimensional non-autonomous Navier-Stokes equation with nonlinear damping in 3D bounded domains. When the external force f0(x,t) is translation compact in Lloc2(R;H), α>0, 72â¤Î²â¤5 and initial data uÏâV, we give a series of uniform estimates on the solutions. Based on these estimates, we prove the family of processes {Uf(t,Ï)}, fâH(f0), is (VÃH(f0),V)-continuous. At the same time, by making use of Ascoli-Arzela theorem, we find {Uf(t,Ï)}, fâH(f0), is (V,H2(Ω))-uniformly compact. So, using semiprocess theory, we obtain the existence of (V,V)-uniform attractor and (V,H2(Ω))-uniform attractor. And we prove the (V,V)-uniform attractor is actually the (V,H2(Ω))-uniform attractor.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xue-li Song, Yan-ren Hou,