A rigorous treatment of `experimental' observations for the two-dimensional Navier-Stokes equations (Q2748043)

The paper deals with the question how many observations are needed to determine a fluid flow throughout the entire domain. NEWLINENEWLINENEWLINEThe author shows that a finite number of point observations (distributed in both space and time) serve to determine the ``fully developed'' flow of a two-dimensional fluid throughout the whole flow domain. With the measurements taken at one fixed time, the results imply that if the flow is resolved on a sufficiently small scale, then its dynamics are entirely determined. Applied to ``experimental'' observations taken randomly from a small neighbourhood of one point in space, but at staggered times, the results also imply a version of Takens' time delay embedding theorem. The mathematical details are given in a separate section.