Parametrising the attractor of the two-dimensional Navier–Stokes equations with a finite number of nodal values

We consider the solutions lying on the global attractor of the two-dimensional Navier–Stokes equations with periodic boundary conditions and analytic forcing. We show that in this case the value of a solution at a finite number of nodes determines elements of the attractor uniquely, proving a conjecture 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.