Publication ahead of print Issue ESAIM: COCV DOI 10.1051/cocv/2009017 Published online 02 July 2009

ESAIM: COCV
DOI: 10.1051/cocv/2009017

Controllability of 3D incompressible Euler equations by a finite-dimensional external force

Hayk Nersisyan

CNRS (UMR 8088), Département de Mathématiques, Université de Cergy-Pontoise, Site de Saint-Martin, 2 avenue Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France. Hayk.Nersisyan@u-cergy.fr

Received October 21, 2008. Revised February 20, 2009. Published online July 2nd, 2009.

Abstract
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control. Moreover, the velocity is approximately controllable. We also prove that 3D Euler system is not exactly controllable by a finite-dimensional external force.

Mathematics Subject Classification. 35Q35, 93C20

Key words: Controllability, 3D incompressible Euler equations, Agrachev-Sarychev method


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