A rigorous treatment of 'experimental' observations for the two-dimensional Navier-Stokes equations

Abstract

Within a fully rigorous framework, this paper 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, they imply a version of Takens' time delay embedding theorem