# Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

ESAIM: Control, Optimisation and Calculus of Variations (2008)

- Volume: 15, Issue: 4, page 934-968
- ISSN: 1292-8119

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topBadra, Mehdi. "Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system." ESAIM: Control, Optimisation and Calculus of Variations 15.4 (2008): 934-968. <http://eudml.org/doc/90945>.

@article{Badra2008,

abstract = { We study the local exponential stabilization of the 2D and 3D
Navier-Stokes equations in a bounded domain, around a given
steady-state flow, by means of a boundary control. We look for a
control so that the solution to the Navier-Stokes equations be a
strong solution. In the 3D case, such solutions may exist if the
Dirichlet control satisfies a compatibility condition with the
initial condition. In order to determine a feedback law satisfying
such a compatibility condition, we consider an extended system
coupling the Navier-Stokes equations with an equation satisfied by
the control on the boundary of the domain. We determine a linear
feedback law by solving a linear quadratic control problem for the
linearized extended system. We show that this feedback law also
stabilizes the nonlinear extended system.
},

author = {Badra, Mehdi},

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

keywords = {Navier-Stokes equation; feedback stabilization;
Dirichlet control; Riccati equation; Dirichlet control},

language = {eng},

month = {10},

number = {4},

pages = {934-968},

publisher = {EDP Sciences},

title = {Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system},

url = {http://eudml.org/doc/90945},

volume = {15},

year = {2008},

}

TY - JOUR

AU - Badra, Mehdi

TI - Feedback stabilization of the 2-D and 3-D Navier-Stokes equations based on an extended system

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2008/10//

PB - EDP Sciences

VL - 15

IS - 4

SP - 934

EP - 968

AB - We study the local exponential stabilization of the 2D and 3D
Navier-Stokes equations in a bounded domain, around a given
steady-state flow, by means of a boundary control. We look for a
control so that the solution to the Navier-Stokes equations be a
strong solution. In the 3D case, such solutions may exist if the
Dirichlet control satisfies a compatibility condition with the
initial condition. In order to determine a feedback law satisfying
such a compatibility condition, we consider an extended system
coupling the Navier-Stokes equations with an equation satisfied by
the control on the boundary of the domain. We determine a linear
feedback law by solving a linear quadratic control problem for the
linearized extended system. We show that this feedback law also
stabilizes the nonlinear extended system.

LA - eng

KW - Navier-Stokes equation; feedback stabilization;
Dirichlet control; Riccati equation; Dirichlet control

UR - http://eudml.org/doc/90945

ER -

## References

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