# Approximate controllability of a hydro-elastic coupled system

Jacques-Louis Lions; Enrique Zuazua

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

- Volume: 1, page 1-15
- ISSN: 1292-8119

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topLions, Jacques-Louis, and Zuazua, Enrique. "Approximate controllability of a hydro-elastic coupled system." ESAIM: Control, Optimisation and Calculus of Variations 1 (2010): 1-15. <http://eudml.org/doc/197373>.

@article{Lions2010,

abstract = {
We analyze the controllability of the motion of a fluid by means of the
action of a vibrating shell coupled at the boundary of the fluid. The
model considered is linear. We study its approximate controllability,
i.e. whether the fluid may reach a dense set of final configurations at
a given time. We show that this problem can be reduced to a unique
continuation question for the Stokes system. We prove that this unique
continuation property holds generically among analytic domains and
therefore, that there is approximate controllability generically. We
also prove that this result fails when Ω is a ball showing
that the analyticity assumption on the domain is not sufficient.
},

author = {Lions, Jacques-Louis, Zuazua, Enrique},

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

keywords = {Hydroelasticity / approximate controllability / coupled system /
spectral decomposition / generic spectral properties; Hydroelasticity; approximate controllability; coupled system; spectral decomposition; generic spectral properties; Stokes system},

language = {eng},

month = {3},

pages = {1-15},

publisher = {EDP Sciences},

title = {Approximate controllability of a hydro-elastic coupled system},

url = {http://eudml.org/doc/197373},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Lions, Jacques-Louis

AU - Zuazua, Enrique

TI - Approximate controllability of a hydro-elastic coupled system

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 1

EP - 15

AB -
We analyze the controllability of the motion of a fluid by means of the
action of a vibrating shell coupled at the boundary of the fluid. The
model considered is linear. We study its approximate controllability,
i.e. whether the fluid may reach a dense set of final configurations at
a given time. We show that this problem can be reduced to a unique
continuation question for the Stokes system. We prove that this unique
continuation property holds generically among analytic domains and
therefore, that there is approximate controllability generically. We
also prove that this result fails when Ω is a ball showing
that the analyticity assumption on the domain is not sufficient.

LA - eng

KW - Hydroelasticity / approximate controllability / coupled system /
spectral decomposition / generic spectral properties; Hydroelasticity; approximate controllability; coupled system; spectral decomposition; generic spectral properties; Stokes system

UR - http://eudml.org/doc/197373

ER -

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