collaborators

5 papers

math.AP2026

A critical note on back-and-forth Data Assimilation Nudging Algorithm

Aseel Farhat, Edriss S. Titi, Collin Victor

This work investigates the effectiveness of the Back-and-Forth Nudging (BFN) data assimilation algorithm, specifically its performance when employing the Azouani-Olson-Titi (AOT) c…

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…

math.AP2025

Upper bounds on the dimension of the global attractor of the 2D Navier-Stokes equations on the plane

Aseel Farhat, Anuj Kumar, Vincent R. Martinez

This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the -pl…