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July  2001, 7(3): 643-657. doi: 10.3934/dcds.2001.7.643

Nodal parametrisation of analytic attractors

Peter K. Friz 1, , I. Kukavica 2, and  James C. Robinson 3,

1. 

Trinity College, Cambridge CB2 1TQ, United Kingdom
2. 

Department of Mathematics,, The University of Southern California, Los Angeles, CA 90089-1113
3. 

Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom

Received  July 2000 Revised  December 2000 Published  April 2001

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 $2$d 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 $2$d Navier-Stokes equations with Dirichlet boundary conditions.
Keywords: embedding theorems., experimental observations, global attractors, Determining nodes.
Mathematics Subject Classification: 35B40, 35B42, 35Q30, 37L30, 76D05, 76F2.
Citation: Peter K. Friz, I. Kukavica, James C. Robinson. Nodal parametrisation of analytic attractors. Discrete & Continuous Dynamical Systems, 2001, 7 (3) : 643-657. doi: 10.3934/dcds.2001.7.643
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