Uniform global attractor of the 3D Navier-Stokes equations

Alexey Cheskidov; Lu Songsong

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Uniform global attractor of the 3D Navier-Stokes equations

Alexey Cheskidov 1,Lu Songsong 2 *

1.Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S Morgan St, Chicago, IL 60607-7045, USA

2.Department of Mathematics,SunYat-sen University, GuangZhou 510275

*Correspondence author

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Funding: none

Opened online:15 February 2012

Accepted by: none

Citation: Alexey Cheskidov,Lu Songsong.Uniform global attractor of the 3D Navier-Stokes equations[OL]. [15 February 2012] http://en.paper.edu.cn/en_releasepaper/content/4463406

The long time behavior of the 3DNavier-Stokes equations with a fixed time-dependent force is investigated . The existence and the structure of the weak uniform (with respect to the initial time) global attractor is obtained. A weak trajectory attractor for such a nonautonomous 3D NSE is also constructed. Furthermore, if the external force is normal and every complete bounded trajectory is strongly continuous, these attractors are strongly compact. To this end, an evolutionary system by a new idea is first constructed. Note that such an evolutionary system may have no suitable symbol space. A open problem is naturally put forward that relates to the uniqueness of the Leray-Hopf weak solutions and the minimality property of the uniform (w.r.t. symbol space) attractor.

Keywords:evolutionary system; uniform globalattractor; Navier-Stokes equations; normal external force

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