A Regularity Criterion for the 3-D Navier-Stokes Equations Based on Finitely Many Observations (Abhishek Balakrishna, USC)
March 23 @ 4:15 pm - 5:15 pm
Abstract: This talk presents a regularity criterion for the three-dimensional Navier–Stokes equations based on finitely many observations of the flow. Motivated by data assimilation, we study a nudging algorithm that incorporates coarse spatial measurements through general interpolation operators.
We show that suitable conditions on the observed data guarantee global regularity of the associated system and yield an exponential tracking property. As a consequence, we obtain a new regularity criterion for weak solutions formulated entirely in terms of finitely many observables, covering modal, volume, and nodal measurements.
