A finite number of point observations which determine a non-autonomous fluid flow

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↦(u(x₁),...,u(x_k)) which is one-to-one between the attractor and its image.