ON THE DIMENSION OF THE ATTRACTORS IN TWO-DIMENSIONAL TURBULENCE

被引：149

作者：

CONSTANTIN, P

FOIAS, C

TEMAM, R

机构：

[1] INDIANA UNIV,DEPT MATH,BLOOMINGTON,IN 47405

[2] UNIV PARIS 11,ANALYSE NUMER,F-91405 ORSAY,FRANCE

来源：

PHYSICA D | 1988年 / 30卷 / 03期

基金：

美国国家科学基金会;

关键词：

FLUID DYNAMICS - MATHEMATICAL TECHNIQUES - Nonlinear Equations;

D O I：

10.1016/0167-2789(88)90022-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations. This estimate is optimal up to a logarithmic correction. The relevance of this estimate to turbulence and related results are both briefly discussed.

引用

页码：284 / 296

页数：13

共 26 条

[1]

BABIN AV, 1983, USP MAT NAUK, V38, P133

[2]

Batchelor G. K., 1969, PHYS FLUIDS, V12, pII, DOI [10.1063/1.1692443, DOI 10.1063/1.1692443]

[3]

Brezis H., 1980, Nonlinear Analysis Theory, Methods & Applications, V4, P677, DOI 10.1016/0362-546X(80)90068-1

[4] GLOBAL LYAPUNOV EXPONENTS, KAPLAN-YORKE FORMULAS AND THE DIMENSION OF THE ATTRACTORS FOR 2D NAVIER-STOKES EQUATIONS [J].