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

Issue		ESAIM: COCV Volume 16, Number 3, July-September 2010


Page(s)		677 - 694
DOI		10.1051/cocv/2009017
Published online		02 July 2009

ESAIM: COCV 16 (2010) 677-694

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: 21 October 2008
Revised: 20 February 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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