7 papers
Reformulation and Interpretation of the Regularity Criterion for 3D NSE Based on Finitely Many Observations
Abhishek Balakrishna, Animikh Biswas
We revisit and sharpen a recent observable regularity criterion for the three-dimensional Navier-Stokes equations on the periodic cube by requiring only finitely many measurements…
A unified theory of existence of suitable weak solutions to the 3D incompressible Navier-Stokes equations for non-decaying initial data
A. Balakrishna, I. Kukavica, W. S. Ożański
We consider any cover of by balls of radius bigger or equal satisfying two conditions: (i) any ball intersects at most other balls, and (ii)…
Inviscid fluid interacting with a nonlinear two-dimensional plate
Abhishek Balakrishna, Igor Kukavica, Boris Muha +1
We address a moving boundary problem that consists of a system of equations modeling an inviscid fluid interacting with a two-dimensional nonlinear Koiter plate at the boundary. We…
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…
Strong Stabilization of a 3D Potential Flow via a Weakly Damped von Karman Plate
Abhishek Balakrishna, Irena Lasiecka, Justin T. Webster
The elimination of aeroelastic instability (resulting in sustained oscillations of bridges, buildings, airfoils) is a central engineering and design issue. Mathematically, this tra…
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…