1 citations · 1 across the 7 of their papers we have counts for
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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…
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…
Data assimilation for the Navier-Stokes equations using local observables
Animikh Biswas, Zachary Bradshaw, Michael S. Jolly
We develop, analyze, and test an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations…
Error Estimates for Deep Learning Methods in Fluid Dynamics
Animikh Biswas, Jing Tian, Suleyman Ulusoy
In this study, we provide error estimates and stability analysis of deep learning techniques for certain partial differential equations including the incompressible Navier-Stokes e…
Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations
Animikh Biswas, Randy Price
In this paper, we provide conditions, \emph{based solely on the observed data}, for the global well-posedness, regularity and convergence of the Azouni-Olson-Titi data assimilation…
Space and time analyticity for inviscid equations of fluid dynamics
Animikh Biswas, Joshua Hudson
We show that solutions to a large class of inviscid equations, in Eulerian variables, extend as holomorphic functions of time, with values in a Gevrey class (thus space-analytic),…