RESEARCH INTERESTS
Nonlinear Partial Differential Equations
Navier-Stokes, Euler and related equations:
Well-posedness and long term dynamics.
Geophysical Fluid Dynamics.
Dynamical Systems and Chaos.
Turbulence Theory.
Data Assimilation
Other Areas
Functional Data Analysis.
Systems Theory, Interpolation Theory and H
^{∞}
Control Theory.
Selected Publications
Continuous Data Assimilation for the Three Dimensional Navier-Stokes Equations
Persistence time of solutions of the three-dimensional Navier-Stokes equations in Sobolev-Gevrey classes,
A. Biswas, J. Hudson and J. Tian,
submitted, arxiv:1912.11192.
Space and time analyticity for inviscid equations of fluid dynamics,,
A. Biswas and J. Hudson,
submitted.
Periodic longitudinal motions of a viscoelastic rod,
A. Biswas and T. I. Seidman,
Pure and Applied Functional Analysis,
vol. 4 (2019), no. 4, 671-683.
Downscaling data assimilation algorithm with applications to statistical solutions of the Navier-Stokes equations,
A. Biswas, C. Foias, C. F. Mondaini and E. S. Titi,
Annales d’lInstitut Henri Poincaré/Analyse non lineaire,
vol. 36 (2019), no. 2, 295–326.
Existence time for the 3D Navier-Stokes equations in a generalized Gevrey class,
A. Biswas, C. Foias and B. Nicolaenko,
Physica D,
vol. 376/377 (2018), 5–14.
Continuous data assimilation for the 2D magnetohydrodynamic equations using one component of the velocity and magnetic fields,
A. Biswas, J. Hudson, A. Larios and Y. Pei,
Asymptotic Analysis,
vol. 108 (2018), no. 1-2, 1-43.
A generalized notion of attractor for the semi-dissipative Boussinesq equations,
A. Biswas, C. Foias and A. Larios,
Annales d’lInstitut Henri Poincaré/Analyse non lineaire,
vol. 34 (2017), no. 2, 381-405.
Higher-order synchronization for a data assimilation algorithm for the 2D Navier-Stokes equations,
A. Biswas and V. Martinez,
Nonlinear Analysis: Real World Applications,
vol. 35 (2017), 132-157.
On Gevrey regularity of the supercritical SQG equation in Besov spaces,
A. Biswas, V. Martinez and P. Silva,
Journal of Functional Analysis,
vol. 269, (2015), no. 10, 3083-3119.
Gevrey regularity for a class of dissipative equations with analytic nonlinearity,
H. Bae and A. Biswas,
Methods and Applications of Analysis,
vol. 22 (2015), no 4. 377-408.
Dissipation length scale estimates for turbulent flows: A Wiener algebra approach,
A. Biswas, M. S. Jolly, V. Martinez and E. S. Titi,
Journal of Nonlinear Science,
24
(2014), no. 3, 441-471.
Gevrey regularity for the supercritical quasi-geostrophic equation,
A. Biswas,
Journal of Differential Equations,
257
(2014), 1753-1772.
Dissipation vs quadratic nonlinearity: From
a priori
energy bound to higher-order regularizing effect,
A. Biswas and E. Tadmor,
Nonlinearity,
27
(2014) no. 3, 545-562.
On the maximal spatial analyticity radius for the 3D Navier-Stokes equations and turbulence,
A. Biswas and C. Foias,
Annali di Matematica Pura et Applicata (4),
193
(2014), no. 3, 739-777.
Analyticity and decay estimates of the Navier-Stokes equations in critical Besov spaces,
H. Bae, A. Biswas and E. Tadmor,
Archives for Rational Mechanics and Analysis,
205
(2012), 963 - 991.