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

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

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Abstract

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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.

How to cite

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Boulakia, 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 -

References

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