Fluid-Structure Interaction: Modelling and mathematical analysis of FSI problems, Existence, uniqueness, singular limits and long time behaviour of the solutions.
Fluid Mechanics: Incompressible, Compressible Navier-Stokes, Hard sphere pressure model.
Control of PDE : Controllability, Stabilizability and Optimal control problem for Fluids and Fluid-Structure interaction models.
Porous Media
Liquid Crystals
D. Breit and A. Roy, Compressible fluids and elastic plates in 2D: A conditional no-contact theorem, 2024. Accepted in PhysicaD: Nonlinear Phenomena. arxiv.org/abs/2411.01994
Brandt, F., Hieber, M. and Roy, A., 2025. Dynamics of the general Q-tensor model interacting with a rigid body. Accepted in SIAM J. Math. Analysis. arxiv.org/abs/2501.01181
E. Feireisl, A. Roy and A. Zarnescu, On the effect of a large cloud of rigid particles on the motion of an incompressible non–Newtonian fluid, J. Math. Fluid Mech., Volume 27, Issue 3, Pages 1–18, 2025. link.springer.com/article/10.1007/s00021-025-00944-0
M. Hieber, Y. Iida, A. Roy and T. Zöchling, The Hydrostatic Lagrangian approach to the Compressible Primitive Equations, Mathematische Annalen, Pages 1-32, 2025. https://doi.org/10.1007/s00208-025-03117-6
T. Binz, M. Hieber and A. Roy, Fluid-Structure Interaction with Porous Media: The Beaver-Joseph condition in the strong sense, J. Differential Equations, Volume 426, 660–689, 2025. https://doi.org/10.1016/j.jde.2025.01.042
B. J. Jin, Š. Nečasova, F. Oschmann and A. Roy, Collision of a solid body with its container in a 3D compressible viscous fluid, J. Differential Equations, Volume 426, Pages 760–781 2025. www.sciencedirect.com/science/article/abs/pii/S002203962500066X
T. Binz, F. Brandt, M. Hieber and A. Roy, Interaction of liquid crystals with a rigid body, Trans. Amer. Math. Soc. 377, 8049–8090, 2024. www.ams.org/journals/tran/2024-377-11/S0002-9947-2024-09242-5/
Z. Geng, A. Roy and A. Zarnescu, Global existence of Weak Solutions for a model of nematic liquid crystal-colloidal interactions, SIAM J. Math. Analysis, Volume 56, No. 4, Pages 4324–4355, 2024. epubs.siam.org/doi/abs/10.1137/23M161149X
E. Feireisl, A. Roy and A. Zarnescu, On the motion of a nearly incompressible viscous fluid containing a small rigid body, Journal of Nonlinear Science, Volume 33, Article No. 9, 2023. link.springer.com/article/10.1007/s00332-023-09949-3
E. Feireisl, A. Roy and A. Zarnescu, On the motion of a small rigid body in a viscous compressible fluid, Communications in Partial Differential Equations, Volume 48, Issue 5, Pages 794–818, 2023. doi.org/10.1080/03605302.2023.2202733
E. Feireisl, A. Roy and A. Zarnescu, On the motion of several small rigid bodies in a viscous incompressible fluid, Journal de Mathématiques Pures et Appliqueés (JMPA), Volume 175, Pages 216–236, 2023. doi.org/10.1016/j.matpur.2023.05.007
Š. Nečasová, M. Ramaswamy, A. Roy and A. Schlömerkemper, Motion of a Rigid body in a Compressible Fluid with Navier-slip boundary condition, J. Differential Equations, Volume 338, Pages 256-320, 2022. doi.org/10.1016/j.jde.2022.07.045
Š. Nečasová, A. Novotný and A. Roy, Compressible Navier-Stokes system with the hard sphere pressure law in an exterior domain, Z. Angew. Math. Phys. (ZAMP), Volume 73, Article No. 197, 2022. link.springer.com/article/10.1007/s00033-022-01809-6
V. Mácha, B. Muha, Š. Nečasová, A. Roy and S. Trifunović, Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange, Communications in Partial Differential Equations, Volume 47, Issue 8, 2022. doi.org/10.1080/03605302.2022.2068425
D. Maity, J. -P. Raymond and A. Roy, Existence and uniqueness of maximal strong solution of a 1D Blood flow in a network of vessels, Nonlinear Analysis: Real World Applications, Volume 63, February 2022, 103405.
D. Mitra, A. Roy and T. Takahashi, Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body, Mathematics of Control, Signals and Systems, 2021.
D. Maity, A. Roy and T. Takahashi, Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation, Nonlinearity 34 (4), 2021, 2659-2687.
M. Caggio, O. Kreml, Š. Nečasová, A. Roy and T. Tang, Measure-valued solutions and weak-strong uniqueness for the incompressible inviscid fluid-rigid body interaction, Journal of Mathematical Fluid Mechanics 23 (3), 2021.
Š. Nečasová, M. Ramaswamy, A. Roy and A. Schlömerkemper, Self-propelled motion of a rigid body inside a density dependent incompressible fluid, Math. Model. Nat. Phenom., 16 (2021) 9.
A. Roy and T. Takahashi, Stabilization of a rigid body moving in a compressible viscous fluid, J. Evol. Equ. 21 (2021), 167–200.
D. Maity, J. -P. Raymond and A. Roy, Maximal-in-time existence and uniqueness of strong solution of a 3d fluid-structure interaction model, SIAM J. Math. Anal., 52(6), 2020, 6338–6378.
M. Ramaswamy, A. Roy and T. Takahashi, Remark on the global null controllability for a viscous Burgers-particle system with particle supported control, Applied Mathematics Letters, September 2020, Volume 107.
A. Roy and T. Takahashi, Local null controllability of a rigid body moving into a Boussinesq flow, Math. Control Relat. Fields, December 2019, Volume 9, Issue 4, 793–836.
M. Ramaswamy, J.-P. Raymond and A.Roy, Boundary feedback stabilization of the Boussinesq system with mixed boundary conditions, J. Differential Equations 266 (2019), no. 7, 4268–4304, 2019.
A. Roy, Wellposedness of Boussinesq system, ENUMATH (2023), 310-319, Springer Nature Switzerland. link.springer.com/chapter/10.1007/978-3-031-86169-7_32
D. Maity, A. Roy, and T. Takahashi, Global Stabilization of a rigid body moving in a compressible viscous fluid. In Fluids Under Control: The 2021 Prague-Sum Workshop Lectures, pp. 111-139. Cham: Springer International Publishing, 2023.link.springer.com/chapter/10.1007/978-3-031-27625-5_4
Š. Nečasová, M. Ramaswamy, A. Roy and A. Schlömerkemper, Motion of several rigid bodies in a compressible fluid-mixed case. Interactions between Elasticity and Fluid Mechanics, EMS Series in Industrial and Applied Mathematics (ESIAM), EMS press, Pages 135-174, 2022. ems.press/books/esiam/242/4626
Mathematical Advances in Geophysical Fluid Dynamics. Oberwolfach Report 19 (2022), no. 4, pp. 2961-3003, EMS press. ems.press/journals/owr/articles/11695861
F. Brandt, C. Mîndrilă and A. Roy, Strong time-periodic solutions to a multilayered fluid-structure interaction problem, 2025. arXiv preprint arXiv:2507.07918.arxiv.org/abs/2507.07918
M. Bravin, E. Feireisl, A. Roy, and A. Zarnescu, On the long time behaviour of a system of several rigid bodies immersed in a viscous fluid, 2025. arXiv preprint arXiv:2505.04372.arxiv.org/abs/2505.04372
F. Brandt and A. Roy, Analysis of stochastic fluid-rigid body dynamics: an approach by stochastic maximal regularity, 2025. arXiv preprint arXiv:2504.14676.arxiv.org/abs/2504.14676
C. Mîndrilă, and A. Roy, Multilayered fluid-structure interactions: existence of weak solutions for time-periodic and initial-value problems, 2024. arXiv preprint arXiv:2501.06820.arxiv.org/abs/2501.06820
M. Bravin, E. Feireisl, A. Roy, and A. Zarnescu, On the collective effect of a large system of heavy particles immersed in a Newtonian fluid, 2024. arXiv preprint arXiv:2407.08595.arxiv.org/abs/2407.08595