Controllability to trajectories of a Ladyzhenskaya model for a viscous incompressible fluid

We consider the controllability of a viscous incompressible fluid modeled by the Navier-Stokes systemwith a nonlinear viscosity. To prove the controllability to trajectories, we linearize around a trajectory andthe corresponding linear system includes a nonlocal spatial term. Our main result is a Ca...

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Bibliographic Details
Published inComptes rendus. Mathématique Vol. 359; no. 6; pp. 719 - 732
Main Authors Guerrero, Sergio, Takahashi, Takéo
Format Journal Article
LanguageEnglish
Published Académie des sciences (Paris) 01.01.2021
Académie des sciences
Subjects
Analysis of PDEs
Mathematics
Optimization and Control
Carleman estimates
viscous incompressible fluid
nonlocal spatial terms
controllability to trajectories
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Summary:We consider the controllability of a viscous incompressible fluid modeled by the Navier-Stokes systemwith a nonlinear viscosity. To prove the controllability to trajectories, we linearize around a trajectory andthe corresponding linear system includes a nonlocal spatial term. Our main result is a Carleman estimatefor the adjoint of this linear system. This estimate yields in a standard way the null controllability of thelinear system and the local controllability to trajectories. Our method to obtain the Carleman estimate iscompletely general and can be adapted to other parabolic systems when a Carleman estimate is available.
ISSN:1778-3569
1631-073X
1778-3569
DOI:10.5802/crmath.202