Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T09:50:20.254Z Has data issue: false hasContentIssue false

Exact boundary controllability of 3-D Euler equation

Published online by Cambridge University Press:  15 August 2002

Olivier Glass*
Affiliation:
Université Paris-Sud, Analyse numérique et EDP, 91405 Orsay, France; Olivier.Glass@math.u-psud.fr.
Get access

Abstract

We prove the exact boundary controllability of the 3-D Euler equation of incompressible inviscid fluids on a regular connected bounded open set when the control operates on an open part of the boundary that meets any of the connected components of the boundary.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bardos, C. and Frisch, U., Finite-time regularity for bounded and unbounded ideal incompressible fluids using Hölder estimates, in Proceedings of the conference held at the university of Paris-Sud Orsay, France. Springer-Verlag, Lectures Notes in Math. 565 (1975) 1-13.
Coron, J.-M., Global Asymptotic Stabilization for controllable systems without drift. Math. Control Signals Systems 5 (1992) 295-312. CrossRef
Coron, J.-M., Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels. C. R. Acad. Sci. Paris Sér. I Math. 317 (1993) 271-276.
Coron, J.-M., On the controllability of 2-D incompressible perfect fluids. J. Math. Pures Appl. 75 (1996) 155-188.
Coron, J.-M., On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions. ESAIM Control Optim. Calc. Var. 1 (1996) 35-75. http://www.emath.fr/cocv/. CrossRef
Glass, O., Exact boundary controllability of 3-D Euler equation of perfect incompressible fluids. C. R. Acad. Sci. Paris Sér. I Math. 325 (1997) 987-992. CrossRef
O. Glass, Contrôlabilité de l'équation d'Euler tridimensionnelle pour les fluides parfaits incompressibles, Séminaire Équations aux Dérivées Partielles, 1997-1998, École polytechnique, Centre de Mathématiques, exposé XV.
Hermann, P. and Kersten, H., Über die stetige Abhängigkeit der Lösung des Neumann-Problems für die Prae-Maxwellschen Gleichungen von ihren Randdaten. Arch. Math. (Basel) 36 (1981) 79-82. CrossRef
Kazhikov, A.V., Note on the formulation of the problem of flow through a bounded region using equations of perfect fluid. PMM USSR 44 (1981) 672-674.
J.-L. Lions, Are there connections between turbulence and controllability?, 9th INRIA International Conference, Antibes (June 12-15, 1990).
R. Temam, Navier-Stokes equations and numerical analysis. North-Holland Pub. (1979).