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math.AP2022
A Novel Regularity Criterion For The three-dimensional Navier-Stokes Equations Based On Finitely many observations
Abhishek Balakrishna, Animikh Biswas
In this paper we present two results: (1) A data assimilation algorithm for the 3D Navier-Stokes equation (3D NSE) using nodal data, and, as a consequence (2) a novel regularity cr…
math.AP2021
Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System
Abhishek Balakrishna, Animikh Biswas
In this paper, we provide conditions, \emph{based solely on the observed velocity data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data ass…
math.AP2020
Large Deflections of A Structurally Damped Panel in A Subsonic Flow
Abhishek Balakrishna, Justin T. Webster
The large deflections of panels in subsonic flow are considered. Specifically, a fully clamped von Karman plate accounting for both rotational inertia in plate filaments and struct…