RESEARCH INTERESTS

• Nonlinear Partial Differential Equations

  Navier-Stokes, Euler and related equations: Well-posedness and long term dynamics. Geophysical Fluid Dynamics and Turbulence Theory. Dynamical Systems and Chaos.

• Data Assimilation
  
  
  
  
  
• Other Areas
  • Functional Data Analysis.
  • Systems Theory, Interpolation Theory and H^∞ Control Theory.

Recent Publications (last five years)

1. Parameter recovery for the Navier-Stokes equations via the determining map Animikh Biswas and Joshua Hudson, submitted.
2. Joint modeling of geometric features of longitudinal process and discrete survival time measured on nested time scales: an application to fecundity studies, Abhisek Saha, Ling Ma, Animikh Biswas and Rajeshwari Sundaram, Statistics in Biosciences (2023). doi:10.1007/s12561-023-09381-x
3. Convergence of a Mobile Data Assimilation Scheme for the 2D Navier-Stokes equations, Animikh Biswas, Zachary Bradshaw and Michael Jolly, Discrete and Continuous Dynamical System, (2023). doi: doi:10.3934/dcds.2023078
4. Determining Map, Data Assimilation and an Observable Regularity Criterion for the Three-Dimensional Boussinesq System, Abhishek Balakrishna and Animikh Biswas, Applied Mathematics and Optimization , vol. 86 (2022), no. 3., Paper Number 28, 53 pp.
5. Error estimates for deep learning methods in fluid dynamics, A. Biswas, J. Tian and S. Ulusoy, Numerische Mathematik, vol. 151 (2022) , no 3., 753-777. doi:10.1007/s00211-022-01294-z
6. Mesh-free interpolant observables for continuous data assimilation, Animikh Biswas, Kenneth R. Brown and Vincent R. Martinez, Annals of Applied Mathematics, vol. 38 (2022), no. 3, 296-355. doi: 10.4208/aam.OA-2022-0006
7. Space and time analyticity for inviscid equations of fluid dynamics, Animikh Biswas and Joshua Hudson, Pure and Applied Functional Analysis, vol. 7 (2022), no. 1, 81-98
8. Continuous data assimilation for the three dimensional Navier-Stokes equations, Animikh Biswas and Randy Price, SIAM J. Math. Anal., vol. 53 (2021), no. 6, 6697-6723
9. Data assimilation for the Navier-Stokes equations using local observables, Animikh Biswas, Zachary Bradshaw and Michael Jolly, SIAM J. Appl. Dyn. Syst., vol. 20 (2021), no. 4, 2174-2203.
10. Persistence time of solutions of the three-dimensional Navier-Stokes equations in Sobolev-Gevrey classes, A. Biswas, J. Hudson and J. Tian, Journal of Differential Equations, vol. 277 (2021), 191-233.
11. 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.
12. 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.

Students

• Abhishek Balakrishna (Co-advisor: Dr. Justin Webster), PhD (2023).
• Randy Price (Co-advisor: Dr. Bedrich Sousedik), PhD (2021).
• Joshua Hudson, PhD (2018).

Grants

• 2015-2019, NSF (Applied Mathematics Program), DMS-1517027, Collaborative Research: Deterministic and statistical relations between the Navier-Stokes equations and its determining forms, PI
• 2013-2015, NSF (Applied Mathematics Program), DMS-1425877, Collaborative Research: Study of turbulence in physical systems through complex singularities and determining modes, PI.
• 2011-2013, NSF (Applied Mathematics Program), DMS-1109532, Collaborative Research: Study of turbulence in physical systems through complex singularities and determining modes, PI.