6 citations · 7 across the 5 of their papers we have counts for
5 papers
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…
Persistence time of solutions of the three-dimensional Navier-Stokes equations in Sobolev-Gevrey classes
Animikh Biswas, Joshua Hudson, Jing Tian
In this paper, we study existence times of strong solutions of the three-dimensional Navier-Stokes equations in time-varying analytic Gevrey classes based on Sobolev spaces $H^s, s…
Gevrey regularity for a class of dissipative equations with analytic nonlinearity
Hantaek Bae, Animikh Biswas
In this paper, we establish Gevrey class regularity of solutions to a class of dissipative equations with an analytic nonlinearity in the whole space. This generalizes the results…