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CMX Lunch Seminar

Wednesday, January 24, 2024
12:00pm to 1:00pm
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Annenberg 213
A regularity criterion for the 3D Navier-Stokes equations based on finitely many observations.
Abhishek Balakrishna, Associate Professor, (RTPC) of Mathematics, University of Southern California,

Data assimilation is a technique that combines observational data with a given model to improve the model's accuracy. We first discuss the application of a particular data assimilation technique (AOT algorithms) to the 3-D Navier-Stokes equation (3D NSE); we then describe how a data assimilated solution approximates the true solution. Then we observe the data assimilated solution is, in fact, regular (i.e., a strong solution) when the observed data satisfies a condition we present for only a finite collection of data. This result suggests a connection between our condition and the regularity of solutions to the actual 3D NSE. We pursue this line of inquiry to confirm this hypothesis, and formulate such a regularity criterion for the 3D NSE purely in terms of finitely-observed data.

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