# Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems

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

- Volume: 1, page 267-302
- ISSN: 1292-8119

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topFabre, Caroline. "Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems." ESAIM: Control, Optimisation and Calculus of Variations 1 (2010): 267-302. <http://eudml.org/doc/197285>.

@article{Fabre2010,

abstract = {
The goal of this article is the study of the approximate controllability
for two approximations of Navier Stokes equations with distributed controls.
The method of proof combines a suitable linearization of the system with a
fixed point argument. We then are led to study the approximate controllability
of linear Stokes systems with potentials. We study both the case where there
is no constraint on the control and the case where we search a control having
one null component. In both cases, the problems is reduced to prove unique
continuation results. This is done by means of Carleman estimates.
},

author = {Fabre, Caroline},

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

keywords = {Linear and nonlinear Stokes equations / controllability /
uniqueness properties / Carleman estimates.; Linear and nonlinear Stokes equations; controllability; uniqueness properties; Carleman estimates; approximate controllability; Navier-Stokes equations; linearized Stokes equation; fixed point theorem},

language = {eng},

month = {3},

pages = {267-302},

publisher = {EDP Sciences},

title = {Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems},

url = {http://eudml.org/doc/197285},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Fabre, Caroline

TI - Uniqueness results for Stokes equations and their consequences in linear and nonlinear control problems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 267

EP - 302

AB -
The goal of this article is the study of the approximate controllability
for two approximations of Navier Stokes equations with distributed controls.
The method of proof combines a suitable linearization of the system with a
fixed point argument. We then are led to study the approximate controllability
of linear Stokes systems with potentials. We study both the case where there
is no constraint on the control and the case where we search a control having
one null component. In both cases, the problems is reduced to prove unique
continuation results. This is done by means of Carleman estimates.

LA - eng

KW - Linear and nonlinear Stokes equations / controllability /
uniqueness properties / Carleman estimates.; Linear and nonlinear Stokes equations; controllability; uniqueness properties; Carleman estimates; approximate controllability; Navier-Stokes equations; linearized Stokes equation; fixed point theorem

UR - http://eudml.org/doc/197285

ER -

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