A rigorous treatment of èxperimental ’ observations for the two - dimensional Navier { Stokes equations

Within a fully rigorous framework, this paper shows that a ­ nite number of point observations (distributed in both space and time) serve to determine the `fully developed’ ®ow of a two-dimensional ®uid throughout the whole ®ow domain. With the measurements taken at one ­ xed time, the results imply that if the ®ow is resolved on a su ̄ ciently 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, they imply a version of Takens’ time delay embedding theorem.