We consider the controllability of a viscous incompressible fluid modeled by the Navier–Stokes system with a nonlinear viscosity. To prove the controllability to trajectories, we linearize around a trajectory and the corresponding linear system includes a nonlocal spatial term. Our main result is a Carleman estimate for the adjoint of this linear system. This estimate yields in a standard way the null controllability of the linear system and the local controllability to trajectories. Our method to obtain the Carleman estimate is completely general and can be adapted to other parabolic systems when a Carleman estimate is available.
Accepté le :
Publié le :
Sergio Guerrero 1 ; Takéo Takahashi 2
CC-BY 4.0
@article{CRMATH_2021__359_6_719_0,
author = {Sergio Guerrero and Tak\'eo Takahashi},
title = {Controllability to trajectories of a {Ladyzhenskaya} model for a viscous incompressible fluid},
journal = {Comptes Rendus. Math\'ematique},
pages = {719--732},
publisher = {Acad\'emie des sciences, Paris},
volume = {359},
number = {6},
year = {2021},
doi = {10.5802/crmath.202},
language = {en},
}
TY - JOUR AU - Sergio Guerrero AU - Takéo Takahashi TI - Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid JO - Comptes Rendus. Mathématique PY - 2021 SP - 719 EP - 732 VL - 359 IS - 6 PB - Académie des sciences, Paris DO - 10.5802/crmath.202 LA - en ID - CRMATH_2021__359_6_719_0 ER -
%0 Journal Article %A Sergio Guerrero %A Takéo Takahashi %T Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid %J Comptes Rendus. Mathématique %D 2021 %P 719-732 %V 359 %N 6 %I Académie des sciences, Paris %R 10.5802/crmath.202 %G en %F CRMATH_2021__359_6_719_0
Sergio Guerrero; Takéo Takahashi. Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid. Comptes Rendus. Mathématique, Volume 359 (2021) no. 6, pp. 719-732. doi : 10.5802/crmath.202. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.202/
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