Sharp Estimates for the Number of Degrees of Freedom for the Damped-Driven 2-D Navier-Stokes Equations

被引：1

作者：

A.A. Ilyin

E.S. Titi

机构：

[1] Keldysh Institute of Applied Mathematics,

[2] Russian Academy of Sciences,undefined

[3] Miusskaya Sq. 4,undefined

[4] 125047,undefined

[5] Moscow,undefined

[6] Department of Mathematics and Department of Mechanical and Aerospace Engineering,undefined

[7] University of California,undefined

[8] Irvine,undefined

[9] CA 92697. Also: Department of Computer Science and Applied Mathematics,undefined

[10] Weizmann Institute of Science,undefined

[11] P.O. Box 26,undefined

[12] Rehovot,undefined

[13] 76100,undefined

来源：

Journal of Nonlinear Science | 2006年 / 16卷

关键词：

Fractal Dimension; Global Attractor; Gulf Stream; Sharp Estimate; Periodic Domain;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We derive upper bounds for the number of asymptotic degrees (determining modes and nodes) of freedom for the two-dimensional Navier-Stokes system and Navier-Stokes system with damping. In the first case we obtain the previously known estimates in an explicit form, which are larger than the fractal dimension of the global attractor. However, for the Navier-Stokes system with damping, our estimates for the number of the determining modes and nodes are comparable to the sharp estimates for the fractal dimension of the global attractor. Our investigation of the damped-driven 2-D Navier-Stokes system is inspired by the Stommel-Charney barotropic model of ocean circulation where the damping represents the Rayleigh friction. We remark that our results equally apply to the viscous Stommel-Charney model.

引用

页码：233 / 253

页数：20

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