# 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.

## Submitted:

Mathematical analysis of the motion of a piston in a fluid with density dependent viscosity, with Vaibhav Kumar Jena and Abu Sufian.

## 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.