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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- 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 (2010): 1-42. <http://eudml.org/doc/90864>.

@article{Boulakia2010,

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; controllability},

language = {eng},

month = {3},

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/90864},

volume = {14},

year = {2010},

}

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

DA - 2010/3//

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; controllability

UR - http://eudml.org/doc/90864

ER -

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