Skip to main content Accessibility help
×
Home
Hostname: page-component-78dcdb465f-hcvhd Total loading time: 7.654 Render date: 2021-04-16T09:05:15.267Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Feedback stabilization of Navier–Stokes equations

Published online by Cambridge University Press:  15 September 2003

Viorel Barbu
Affiliation:
Department of Mathematics, “Al.I. Cuza" University, 6600 Iasi, Romania; barbu@uaic.ro.
Get access

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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2003

Access options

Get access to the full version of this content by using one of the access options below.

References

Abergel, F. and Temam, R., On some control problems in fluid mechanics. Theoret. Comput. Fluid Dynam. 1 (1990) 303-325. CrossRef
V. Barbu, Mathematical Methods in Optimization of Differential Systems. Kluwer, Dordrecht (1995).
Barbu, V., Local controllability of Navier-Stokes equations. Adv. Differential Equations 6 (2001) 1443-1462.
Barbu, V., The time optimal control of Navier-Stokes equations. Systems & Control Lett. 30 (1997) 93-100. CrossRef
Barbu, V. and Sritharan, S., $H^{\infty}$ -control theory of fluid dynamics. Proc. Roy. Soc. London 454 (1998) 3009-3033. CrossRef
Barbu, V. and Sritharan, S., Flow invariance preserving feedback controller for Navier-Stokes equations. J. Math. Anal. Appl. 255 (2001) 281-307. CrossRef
Th.R. Bewley, S. Liu, Optimal and robust control and estimation of linear path to transition. J. Fluid Mech. 365 (1998) 305-349. CrossRef
A. Bensoussan, G. Da Prato, M.C. Delfour and S.K. Mitter, Representation and Control of Infinite Dimensional Systems. Birkhäuser, Boston, Bassel, Berlin (1992).
Cao, C., Kevrekidis, I.G. and Titi, E.S., Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. Indiana Univ. Math. J. 50 (2001) 37-96. CrossRef
P. Constantin and C. Foias, Navier-Stokes Equations. University of Chicago Press, Chicago, London (1989).
Coron, J.M., On the controllability for the 2-D incompresssible Navier-Stokes equations with the Navier slip boundary conditions. ESAIM: COCV 1 (1996) 33-75.
Coron, J.M., 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. CrossRef
Coron, J.M. and Fursikov, A., Global exact controllability of the 2-D Navier-Stokes equations on a manifold without boundary. Russian J. Math. Phys. 4 (1996) 429-448.
Imanuvilov, O.A., Local controllability of Navier-Stokes equations. ESAIM: COCV 3 (1998) 97-131. CrossRef
Imanuvilov, O.A., On local controllability of Navier-Stokes equations. ESAIM: COCV 6 (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).

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 54 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 16th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Feedback stabilization of Navier–Stokes equations
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Feedback stabilization of Navier–Stokes equations
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Feedback stabilization of Navier–Stokes equations
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *