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

Fabre, 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 -