Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions

Sergio Guerrero

ESAIM: Control, Optimisation and Calculus of Variations (2006)

  • Volume: 12, Issue: 3, page 484-544
  • ISSN: 1292-8119

Abstract

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In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.

How to cite

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Guerrero, Sergio. "Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions." ESAIM: Control, Optimisation and Calculus of Variations 12.3 (2006): 484-544. <http://eudml.org/doc/249676>.

@article{Guerrero2006,
abstract = { In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system. },
author = {Guerrero, Sergio},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Navier-Stokes system; controllability; slip.; slip},
language = {eng},
month = {6},
number = {3},
pages = {484-544},
publisher = {EDP Sciences},
title = {Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions},
url = {http://eudml.org/doc/249676},
volume = {12},
year = {2006},
}

TY - JOUR
AU - Guerrero, Sergio
TI - Local exact controllability to the trajectories of the Navier-Stokes system with nonlinear Navier-slip boundary conditions
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2006/6//
PB - EDP Sciences
VL - 12
IS - 3
SP - 484
EP - 544
AB - In this paper we deal with the local exact controllability of the Navier-Stokes system with nonlinear Navier-slip boundary conditions and distributed controls supported in small sets. In a first step, we prove a Carleman inequality for the linearized Navier-Stokes system, which leads to null controllability of this system at any time T>0. Then, fixed point arguments lead to the deduction of a local result concerning the exact controllability to the trajectories of the Navier-Stokes system.
LA - eng
KW - Navier-Stokes system; controllability; slip.; slip
UR - http://eudml.org/doc/249676
ER -

References

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