Data assimilation for the Navier-Stokes equations using local observables

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https://epubs.siam.org/doi/10.1137/20M136058X

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https://doi.org/10.1137/20M136058X

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UMBC Mathematics and Statistics Department
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https://orcid.org/0000-0001-8594-0568

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2021-10-28

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journal articles
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Biswas, Animikh, Zachary Bradshaw, and Michael S. Jolly. “Data Assimilation for the Navier--Stokes Equations Using Local Observables.” SIAM Journal on Applied Dynamical Systems 20, no. 4 (January 2021): 2174–2203. https://doi.org/10.1137/20M136058X.

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Abstract

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