Feedback stabilization of Navier–Stokes equations

Viorel Barbu

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

  • Volume: 9, page 197-205
  • ISSN: 1292-8119

Abstract

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One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation.

How to cite

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Barbu, Viorel. "Feedback stabilization of Navier–Stokes equations." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 197-205. <http://eudml.org/doc/90689>.

@article{Barbu2010,
abstract = { One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation. },
author = {Barbu, Viorel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Navier–Stokes system; Riccati equation; linearized system; steady-state solution; weak solution.; Navier-Stokes system; steady-state solution; weak solution},
language = {eng},
month = {3},
pages = {197-205},
publisher = {EDP Sciences},
title = {Feedback stabilization of Navier–Stokes equations},
url = {http://eudml.org/doc/90689},
volume = {9},
year = {2010},
}

TY - JOUR
AU - Barbu, Viorel
TI - Feedback stabilization of Navier–Stokes equations
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 9
SP - 197
EP - 205
AB - One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a LQ control problem associated with the linearized equation.
LA - eng
KW - Navier–Stokes system; Riccati equation; linearized system; steady-state solution; weak solution.; Navier-Stokes system; steady-state solution; weak solution
UR - http://eudml.org/doc/90689
ER -

References

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  12. J.M. Coron, On the null asymptotic stabilization of the 2-D incompressible Euler equations in a simple connected domain. SIAM J. Control Optim.37 (1999) 1874-1896.  Zbl0954.76010
  13. J.M. Coron and A. Fursikov, Global exact controllability of the 2-D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys.4 (1996) 429-448.  Zbl0938.93030
  14. O.A. Imanuvilov, Local controllability of Navier-Stokes equations. ESAIM: COCV3 (1998) 97-131.  Zbl1052.93502
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  17. R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis. SIAM Philadelphia (1983).  Zbl0522.35002

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