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We develop, analyze, and test an approximate, global dataassimilation/synchronization algorithm based on purely local observations forthe two-dimensional Navier-Stokes equations on the torus. We prove that, forany error threshold, if the reference flow is analytic with sufficiently largeanalyticity radius, then it can be recovered within that threshold. Numericalcomputations are included to demonstrate the effectiveness of this approach, aswell as variants with data on moving subdomains. In particular, we demonstratenumerically that machine precision synchronization is achieved for mobile datacollected from a small fraction of the domain.

Data assimilation for the Navier-Stokes equations using local observables