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

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 16, Issue: 3, page 677-694
- ISSN: 1292-8119

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topNersisyan, Hayk. "Controllability of 3D incompressible Euler equations by a finite-dimensional external force." ESAIM: Control, Optimisation and Calculus of Variations 16.3 (2010): 677-694. <http://eudml.org/doc/250730>.

@article{Nersisyan2010,

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.
},

author = {Nersisyan, Hayk},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Controllability; 3D incompressible Euler equations; Agrachev-Sarychev method; controllability},

language = {eng},

month = {7},

number = {3},

pages = {677-694},

publisher = {EDP Sciences},

title = {Controllability of 3D incompressible Euler equations by a finite-dimensional external force},

url = {http://eudml.org/doc/250730},

volume = {16},

year = {2010},

}

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

DA - 2010/7//

PB - EDP Sciences

VL - 16

IS - 3

SP - 677

EP - 694

AB -
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.

LA - eng

KW - Controllability; 3D incompressible Euler equations; Agrachev-Sarychev method; controllability

UR - http://eudml.org/doc/250730

ER -

## References

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- A. Shirikyan, Approximate controllability of three-dimensional Navier–Stokes equations. Comm. Math. Phys.266 (2006) 123–151.
- A. Shirikyan, Exact controllability in projections for three-dimensional Navier–Stokes equations. Ann. Inst. H. Poincaré, Anal. Non Linéaire24 (2007) 521–537.
- A. Shirikyan, Euler equations are not exactly controllable by a finite-dimensional external force. Physica D237 (2008) 1317–1323.
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