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Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values. (English) Zbl 1076.35090

Summary: 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.

MSC:

35Q30 Navier-Stokes equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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