Nodal parametrisation of analytic attractors

被引：12
作者：
Friz, PK [1 ]
Kukavica, I
Robinson, JC
机构：
[1] Univ Cambridge Trinity Coll, Cambridge CB2 1TQ, England
[2] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA
[3] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2001年 / 7卷 / 03期
关键词：
determining nodes; global attractors; experimental observations; embedding theorems;
D O I：
10.3934/dcds.2001.7.643
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Friz and Robinson showed that analytic global attractors consisting of periodic functions can be parametrised using the values of the solution at a finite number of points throughout the domain, a result applicable to the 2d Navier-Stokes equations with periodic boundary conditions. In this paper we extend the argument to cover any attractor consisting of analytic functions; in particular we are now able to treat the 2d Navier-Stokes equations with Dirichlet boundary conditions.
引用
收藏
页码：643 / 657
页数：15
相关论文
共 31 条
[1]  
[Anonymous], 1974, REAL COMPLEX ANAL
[2]  
Babin A.V., 1992, ATTRACTORS EVOLUTION
[3]   GLOBAL LYAPUNOV EXPONENTS, KAPLAN-YORKE FORMULAS AND THE DIMENSION OF THE ATTRACTORS FOR 2D NAVIER-STOKES EQUATIONS [J].
CONSTANTIN, P ;
FOIAS, C .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (01) :1-27
[4]   ON THE DIMENSION OF THE ATTRACTORS IN TWO-DIMENSIONAL TURBULENCE [J].
CONSTANTIN, P ;
FOIAS, C ;
TEMAM, R .
PHYSICA D, 1988, 30 (03) :284-296
[5]   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
[6]  
Constantin P., 1988, Chicago Lectures in Mathematics, DOI DOI 10.7208/CHICAGO/9780226764320.001.0001
[7]  
Eden A., 1994, Research in Applied Mathematics
[8]  
Falconer K. J., 1985, The geometry of fractal sets
[9]  
FOIAS C, 1984, MATH COMPUT, V43, P117, DOI 10.1090/S0025-5718-1984-0744927-9
[10]  
Foias C, 1996, INDIANA U MATH J, V45, P603
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