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.

Classification: 35Q35, 93C20

Keywords: controllability, 3D incompressible Euler equations, Agrachev-Sarychev method

@article{COCV_2010__16_3_677_0, author = {Nersisyan, Hayk}, title = {Controllability of 3D incompressible Euler equations by a finite-dimensional external force}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {16}, number = {3}, year = {2010}, pages = {677-694}, doi = {10.1051/cocv/2009017}, zbl = {1193.35141}, mrnumber = {2674632}, language = {en}, url = {http://www.numdam.org/item/COCV_2010__16_3_677_0} }

Nersisyan, Hayk. Controllability of 3D incompressible Euler equations by a finite-dimensional external force. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 3, pp. 677-694. doi : 10.1051/cocv/2009017. http://www.numdam.org/item/COCV_2010__16_3_677_0/

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