Controllability of 3D incompressible Euler equations by a finite-dimensional external force
CNRS (UMR 8088), Département de Mathématiques,
Université de Cergy-Pontoise, Site de Saint-Martin,
2 avenue Adolphe Chauvin,
95302 Cergy-Pontoise Cedex, France.
Revised: 20 February 2009
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
© EDP Sciences, SMAI, 2009