3 papers
math.AP2025
On the nudging approach to continuous data assimilation in the limit of infinite error feedback gain
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
This article studies the intimate relationship between two filtering algorithms for continuous data assimilation, the synchronization filter and the nudging filter, in the paradigm…
math.AP2025
Determining Modes, State Reconstruction, and Intertwinement: A Synchronization Framework
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
This article studies the interrelation between the determining modes property in the two-dimensional (2D) Navier-Stokes equations (NSE) of incompressible fluids and the reconstruct…
math.AP2025
Determining Modes, State Reconstruction, and Intertwinement: Existence of Self-Synchronizing Intertwinements
Elizabeth Carlson, Aseel Farhat, Vincent R. Martinez +1
In the companion paper of the authors, a general synchronization framework was developed in the paradigmatic context of the 2D Navier-Stokes equations that allows one to precisely…