# Local null controllability of a two-dimensional fluid-structure interaction problem

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 14, Issue: 1, page 1-42
- ISSN: 1292-8119

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topBoulakia, Muriel, and Osses, Axel. "Local null controllability of a two-dimensional fluid-structure interaction problem." ESAIM: Control, Optimisation and Calculus of Variations 14.1 (2008): 1-42. <http://eudml.org/doc/245642>.

@article{Boulakia2008,

abstract = {In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given $T > 0$, the system can be driven at rest and the structure to its reference configuration at time $T$. To show this result, we first consider a linearized system. Thanks to an observability inequality obtained from a Carleman inequality, we prove an optimal controllability result with a regular control. Next, with the help of Kakutani’s fixed point theorem and a regularity result, we pass to the nonlinear problem.},

author = {Boulakia, Muriel, Osses, Axel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {controllability; fluid-solid interaction; Navier-Stokes equations; Carleman estimates},

language = {eng},

number = {1},

pages = {1-42},

publisher = {EDP-Sciences},

title = {Local null controllability of a two-dimensional fluid-structure interaction problem},

url = {http://eudml.org/doc/245642},

volume = {14},

year = {2008},

}

TY - JOUR

AU - Boulakia, Muriel

AU - Osses, Axel

TI - Local null controllability of a two-dimensional fluid-structure interaction problem

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2008

PB - EDP-Sciences

VL - 14

IS - 1

SP - 1

EP - 42

AB - In this paper, we prove a controllability result for a fluid-structure interaction problem. In dimension two, a rigid structure moves into an incompressible fluid governed by Navier-Stokes equations. The control acts on a fixed subset of the fluid domain. We prove that, for small initial data, this system is null controllable, that is, for a given $T > 0$, the system can be driven at rest and the structure to its reference configuration at time $T$. To show this result, we first consider a linearized system. Thanks to an observability inequality obtained from a Carleman inequality, we prove an optimal controllability result with a regular control. Next, with the help of Kakutani’s fixed point theorem and a regularity result, we pass to the nonlinear problem.

LA - eng

KW - controllability; fluid-solid interaction; Navier-Stokes equations; Carleman estimates

UR - http://eudml.org/doc/245642

ER -

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## Citations in EuDML Documents

top- Yuning Liu, Takéo Takahashi, Marius Tucsnak, Single input controllability of a simplified fluid-structure interaction model
- Jérôme Le Rousseau, Gilles Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
- Jérôme Le Rousseau, Gilles Lebeau, On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

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