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
Mots clés : 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},
pages = {677--694},
publisher = {EDP-Sciences},
volume = {16},
number = {3},
year = {2010},
doi = {10.1051/cocv/2009017},
zbl = {1193.35141},
mrnumber = {2674632},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2009017/}
}
TY - JOUR AU - Nersisyan, Hayk TI - Controllability of 3D incompressible Euler equations by a finite-dimensional external force JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2010 DA - 2010/// SP - 677 EP - 694 VL - 16 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2009017/ UR - https://zbmath.org/?q=an%3A1193.35141 UR - https://www.ams.org/mathscinet-getitem?mr=2674632 UR - https://doi.org/10.1051/cocv/2009017 DO - 10.1051/cocv/2009017 LA - en ID - COCV_2010__16_3_677_0 ER -
Nersisyan, Hayk. Controllability of 3D incompressible Euler equations by a finite-dimensional external force. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 677-694. doi : 10.1051/cocv/2009017. http://www.numdam.org/articles/10.1051/cocv/2009017/
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