The Lorenz equation as a metaphor for the Navier-Stokes equations

被引：19

作者：

Foias, C ^{[1
]}

Jolly, MS

Kukavica, I

Titi, ES

机构：

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

[2] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

[3] Univ Calif Irvine, Dept Math, Irvine, CA 92697 USA

[4] Univ Calif Irvine, Dept Mech & Aerosp Engn, Irvine, CA 92697 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2001年 / 7卷 / 02期

关键词：

Navier-Stokes; Lorenz equation; statistical solutions;

D O I：

10.3934/dcds.2001.7.403

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Three approaches for the rigorous study of the 2D Navier-Stokes equations (NSE) are applied to the Lorenz system. Analysis of time averaged solutions leads to a description of invariant probability measures on the Lorenz attractor which is much more complete than what is known for the NSE. As is the case for the NSE, solutions on the Lorenz attractor are analytic in a strip about the real time axis. Rigorous estimates are combined with numerical computation of Taylor coefficients to estimate the width of this strip. Approximate inertial forms originally developed for the NSE are analyzed for the Lorenz system, and the dynamics for the latter are completely described.

引用

页码：403 / 429

页数：27

共 33 条

[1]

CONSTANTIN P, 1985, MEM AM MATH SOC, V53, P1

[2] Dirichlet quotients and 2D periodic Navier-Stokes equations [J].

Constantin, P ;

Foias, C ;

Kukavica, I ;

Majda, AJ .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1997, 76 (02) :125-153

[3] GENERALIZED LORENTZ SYSTEM [J].

CURRY, JH .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 60 (03) :193-204

[4] Exploring invariant sets and invariant measures [J].

Dellnitz, M ;

Hohmann, A ;

Junge, O ;

Rumpf, M .

CHAOS, 1997, 7 (02) :221-228

[5]

Dunford N., 1958, Linear Operators. Part II: Spectral Theory

[6]

Eden A., 1991, J. Dyn. Differ. Equ, V3, P133

[7]

FOIAS C, 1979, J MATH PURE APPL, V58, P339

[8] INERTIAL MANIFOLDS FOR NONLINEAR EVOLUTIONARY EQUATIONS [J].

FOIAS, C ;

SELL, GR ;

TEMAM, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1988, 73 (02) :309-353

[9] ON THE NUMERICAL ALGEBRAIC-APPROXIMATION OF GLOBAL ATTRACTORS [J].

FOIAS, C ;

JOLLY, MS .

NONLINEARITY, 1995, 8 (03) :295-319

[10] Localization of attractors by their analytic properties [J].

Foias, C ;

Jolly, MS ;

Kukavica, I .

NONLINEARITY, 1996, 9 (06) :1565-1581

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