Parametrising the attractor of the two-dimensional Navier-Stokes equationswith a finite number of nodal values

We consider the solutions lying on the global attractor of the two-dimensio nal Navier-Stokes equations with periodic boundary conditions and analytic forcing. We show that in this case the value of a solution at a finite numb er of nodes determines elements of the attractor uniquely, proving a conjec ture due to Foias and Temam. Our results also hold for the complex Ginzburg -Landau equation, the Kuramoto-Sivashinsky equation, and reaction-diffusion equations with analytic nonlinearities. (C) 2001 Elsevier Science B.V. All rights reserved.