# Debayan Maity

Reader (Assistant Professor)

TIFR Centre for Applicable Mathematics

Bangalore, 560065, India

Email: debayan [ AT ] tifrbng [ DOT ] res [ DOT ] in

## Research Interests

Fluid-solid interaction problems

Control and stabilization of PDE's

# Publications

## Articles:

Local stabilization of the compressible Navier–Stokes system, around null velocity, in one dimension, with Shirshendu Chowdhury, Mythily Ramaswamy and Jean-Pierre Raymond, Journal of Differential Equations, Volume 259, Issue 1, 5 July 2015, Pages 371-407.

Some controllability results for linearized compressible Navier-Stokes system, ESAIM Control Optim. Calc. Var 21 (2015), no. 4, 1002-1028.

Analysis of a system modelling the motion of a piston in a viscous gas, with Takéo Takahashi and Marius Tucsnak, Journal of Mathematical Fluid Mechanics, 19 (2017), no. 3, 551-579.

Feedback stabilization of the incompressible Navier-Stokes equations coupled with a damped elastic system in two dimensions, with Jean-Pierre Raymond, Journal of Mathematical Fluid Mechanics, 19 (2017), no. 4, 773-805.

Lp-Lq maximal regularity for some operators associated with linearized incompressible fluid-rigid body problems, with Marius Tucsnak, Mathematical analysis in fluid mechanics - selected recent results, vol. 710 of Contemp. Math., Amer. Math. Soc., Providence, RI, 2018, pp. 175 - 201.

Controllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion, with Marius Tucsnak and Enrique Zuazua, Journal de Mathématiques Pures et Appliquées, (9) 129 (2019), 153–179.

Analysis of a simplified model of rigid structure floating in a viscous fluid, with Jorge San Martín, Takéo Takahashi and Marius Tucsnak, Journal of Nonlinear Science, 29 (2019), no. 5, 1975–2020.

Mathematical analysis of the motion of a rigid body in a compressible Navier-Stokes-Fourier fluid, with Bernhard H. Haak, Takéo Takahashi and Marius Tucsnak, Mathematische Nachrichten, 292 (2019), no. 9, 1972-2017.

Lack of null controllability of viscoelastic flows, with Debanjana Mitra and Michael Renardy, ESAIM: Control, Optimisation and Calculus of Variations, 25 (2019), Art. 60, 26 pp.

On the null controllability of the Lotka-Mckendrick system, Mathematical Control and Related Fields, 2019, 9(4): 719-728.

Controllability of a class of infinite dimensional systems with age structure, with Marius Tucsnak and Enrique Zuazua, Control and Cybernatics (special issue in honour of Günter Leugering), 48 (2019), no. 2, 231–260.

Maximal-in-time existence of strong solutions of a 3D fluid structure interaction model, with Jean -Pierre Raymond and Arnab Roy, SIAM J. Math. Anal, 52 (2020), no. 6, 6338–6378.

Existence and uniqueness of strong solutions for the system of interaction between a compressible Navier-Stokes-Fourier fluid and a damped plate equation, with Takéo Takahashi, Nonlinear Anal. Real World Appl. Paper No. 103267, 34 pp.

Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation, with Arnab Roy and Takéo Takahashi, Nonlinearity, 34 (2021), no. 4, 2659–2687.

Lp theory for the interaction between the incompressible Navier-Stokes system and a damped plate, with Takéo Takahashi, J. Math. Fluid Mech, no. 4, Paper No. 103, 23 pp.

Existence and uniqueness of maximal strong solution of a 1d blood flow in a network of vessels, with Jean-Pierre Raymond and Arnab Roy, Nonlinear Anal. Real World Appl, 63 (2022), Paper No. 103405, 33 pp.

Lack of null controllability of one dimensional linear coupled transport-parabolic system with variable coefficients, with Sakil Ahmed and Debanjana Mitra, Journal of Differential Equations, Volume 320, 25 May 2022, Pages 64-113.

Lack of complete stabilizability of some coupled ODE-parabolic system, with Debanjana Mitra and Mythily Ramaswamy, Math. Rep. (Bucur.) (special issue in honour of Marius Tucsnak), 24(74), 1-2 (2022), 241-267.

Large time behaviour for the motion of a solid in a viscous incompressible fluid, with Sylvain Ervedoza and Marius Tucsnak, Mathematische Annalen, (2023), no. 1-2, 631–691.

Control of the Stefan problem in a periodic box, with Borjan Geshkovski, Math. Models Methods Appl. Sci, Vol. 33, No. 03, pp. 547-608 (2023).

Motion of rigid bodies of arbitrary shape in a viscous incompressible fluid: wellposedness and large time behaviour, with Marius Tucsnak, J. Math. Fluid Mech, 25, Article number: 74 (2023).

Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition, with Takéo Takahashi, Discrete and Continuous Dynamical Systems, 2024, 44(3): 718-742.

Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity, with Vaibhav Kumar Jena and Abu Sufian, Journal of Evolution Equations, 24, article number 76, (2024).Volume 24, article number 76, (2024) Volume 24, article number 76, (2024)

## Submitted:

Regularity of weak solutions of a fluid-rigid body interaction system in a bounded domain under the Prodi-Serrin condition, with Takéo Takahashi.

## Book Chapters:

A maximal regularity approach to the analysis of some particulate flows, with Marius Tucsnak, Particles in Flows, 1 -75, Adv. Math. Fluid Mech., Birkhäuser/Springer, Cham, 2017.

Global Stabilization of a rigid body moving in a compressible viscous fluid, with Arnab Roy and Takéo Takahashi, Fluids Under Control, pp 111–139, Adv. Math. Fluid Mech., Birkhäuser/Springer, Cham, 2023.