# Feedback stabilization of Navier–Stokes equations

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

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

## Access Full Article

top## Abstract

top## How to cite

topBarbu, 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

top- F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Comput. Fluid Dynam.1 (1990) 303-325. Zbl0708.76106
- V. Barbu, Mathematical Methods in Optimization of Differential Systems. Kluwer, Dordrecht (1995).
- V. Barbu, Local controllability of Navier-Stokes equations. Adv. Differential Equations6 (2001) 1443-1462. Zbl1034.35012
- V. Barbu, The time optimal control of Navier-Stokes equations. Systems & Control Lett.30 (1997) 93-100. Zbl0898.49011
- V. Barbu and S. Sritharan, ${H}^{\infty}$-control theory of fluid dynamics. Proc. Roy. Soc. London454 (1998) 3009-3033.
- V. Barbu and S. Sritharan, Flow invariance preserving feedback controller for Navier-Stokes equations. J. Math. Anal. Appl.255 (2001) 281-307. Zbl1073.93030
- Th.R. Bewley and S. Liu, Optimal and robust control and estimation of linear path to transition. J. Fluid Mech.365 (1998) 305-349. Zbl0924.76028
- A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Birkhäuser, Boston, Bassel, Berlin (1992). Zbl0781.93002
- C. Cao, I.G. Kevrekidis and E.S. Titi, Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. Indiana Univ. Math. J.50 (2001) 37-96. Zbl0997.35048
- P. Constantin and C. Foias, Navier-Stokes Equations. University of Chicago Press, Chicago, London (1989). Zbl0687.35071
- J.M. Coron, On the controllability for the 2-D incompresssible Navier-Stokes equations with the Navier slip boundary conditions. ESAIM: COCV1 (1996) 33-75. Zbl0872.93040
- 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
- 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
- O.A. Imanuvilov, Local controllability of Navier-Stokes equations. ESAIM: COCV3 (1998) 97-131. Zbl1052.93502
- O.A. Imanuvilov, On local controllability of Navier-Stokes equations. ESAIM: COCV6 (2001) 49-97.
- I. Lasiecka and R. Triggianni, Control Theory for Partial Differential Equations: Continuous and Approximation Theories, Encyclopedia of Mathematics and its Applications. Cambridge University Press (2000).
- R. Temam, Navier-Stokes Equations and Nonlinear Functional Analysis. SIAM Philadelphia (1983). Zbl0522.35002

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.