Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Nodal parametrisation of analytic attractors

Pages: 643 - 657, Volume 7, Issue 3, July 2001      doi:10.3934/dcds.2001.7.643

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Peter K. Friz - Trinity College, Cambridge CB2 1TQ, United Kingdom (email)
I. Kukavica - Department of Mathematics,, The University of Southern California, Los Angeles, CA 90089-1113, United States (email)
James C. Robinson - Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email)

Abstract: 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:  Determining nodes, global attractors, experimental observations, embedding theorems.
Mathematics Subject Classification:  35B40, 35B42, 35Q30, 37L30, 76D05, 76F20.

Received: July 2000;      Revised: December 2000;      Published: April 2001.