UNSPECIFIED. (2001) A finite number of point observations which determine a non-autonomous fluid flow. NONLINEARITY, 14 (4). pp. 673-682. ISSN 0951-7715

Abstract

We show that a finite number of point observations serve to determine the flow field throughout the entire domain for certain two-dimensional (2D) flows. In particular, we consider the 2D Navier-Stokes equations with periodic boundary conditions and a time-dependent forcing which is analytic in space. Using the theory of non-autonomous attractors developed by Chepyzhov and Vishik, and the theory of point observations developed by Friz and Robinson, we show that almost every choice of a sufficient number of 'nodes' in the domain gives an evaluation map u vertical bar --> (u(x(1)),..., u(x(k))) which is one-to-one between the attractor and its image.

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