Stabilization of a rigid body moving in a compressible viscous fluid

Roy, Arnab; Takahashi, Takéo

doi:10.1007/s00028-020-00574-1

Cited by 14 publications

(21 citation statements)

References 13 publications

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“…A few results are available on the motion of a rigid structure in a compressible fluid with Dirichlet boundary conditions. The existence of strong solutions in the L 2 -framework for small data up to a collision was shown in [1,31]. The existence of strong solutions in the L p setting based on R-bounded operators was applied in the barotropic case [21] and in the full system [19].…”

Section: Introductionmentioning

confidence: 99%

Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

Nečasová

Ramaswamy²,

Roy³

et al. 2022

Journal of Differential Equations

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Section: Introductionmentioning

confidence: 99%

Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

Nečasová

Ramaswamy²,

Roy³

et al. 2022

Journal of Differential Equations

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“…Note that the corresponding control problem involves two controls, one for the fluid and one for the structure. For the stabilization of fluid-structure interaction systems, one can quote some results: [51], [4] (for the case of a damped beam), [56], [54], [3], [2] (for the case of a rigid body).…”

Section: Introductionmentioning

confidence: 99%

Controllability of a Stokes system with a diffusive boundary condition

Takahashi¹,

Buffe²

2022

ESAIM: COCV

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We are interested by the controllability of a fluid-structure interaction system where the fluid is viscous and incompressible and where the structure is elastic and located on a part of the boundary of the fluid's domain. In this article, we simplify this system by considering a linearization and by replacing the wave/plate equation for the structure by a heat equation. We show that the corresponding system coupling the Stokes equations with a heat equation at its boundary is null-controllable. The proof is based on Carleman estimates and interpolation inequalities. One of the Carleman estimates corresponds to the case of Ventcel boundary conditions. This work can be seen as a first step to handle the real system where the structure is modeled by the wave or the plate equation.

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“…In [24], the structure is a deformable beam located at the boundary of the fluid domain and the author obtains the local stabilization of the corresponding system. In [35] (respectively [31]), an open stabilization result is proved in the case of rigid ball moving into viscous incompressible (respectively compressible) fluid with a spring-damper type control.…”

Section: Introductionmentioning

confidence: 99%

Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

Mitra

Roy

Takahashi

2021

Math. Control Signals Syst.

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We study control properties of a linearized fluid-structure interaction system, where the structure is a rigid body and where the fluid is a viscoelastic material. We establish the approximate controllability and the exponential stabilizability for the velocities of the fluid and of the rigid body and for the position of the rigid body. In order to prove this, we prove a general result for this kind of systems that generalizes in particular the case without structure. The exponential stabilization of the system is obtained with a finite-dimensional feedback control acting only on the momentum equation on a subset of the fluid domain and up to some rate that depends on the coefficients of the system. We also show that, as in the case without structure, the system is not exactly null-controllable in finite time.

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Stabilization of a rigid body moving in a compressible viscous fluid

Cited by 14 publications

References 13 publications

Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

Motion of a rigid body in a compressible fluid with Navier-slip boundary condition

Controllability of a Stokes system with a diffusive boundary condition

Approximate controllability and stabilizability of a linearized system for the interaction between a viscoelastic fluid and a rigid body

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