Displaying similar documents to “Feedback stabilization of Navier–Stokes equations”

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

Mehdi Badra (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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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...

On exact controllability for the Navier-Stokes equations

O. Yu. Imanuvilov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the local exact controllability problem for the Navier-Stokes equations that describe an incompressible fluid flow in a bounded domain with control distributed in an arbitrary fixed subdomain. The result that we obtain in this paper is as follows. Suppose that we have a given stationary point of the Navier-Stokes equations and our initial condition is sufficiently close to it. Then there exists a locally distributed control such that in a given moment of time the solution of...

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

Mehdi Badra (2008)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

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...

Feedback stabilization of Navier–Stokes equations

Viorel Barbu (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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One proves that the steady-state solutions to Navier–Stokes equations with internal controllers are locally exponentially stabilizable by linear feedback controllers provided by a control problem associated with the linearized equation.

Distributed control for multistate modified Navier-Stokes equations

Nadir Arada (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to establish necessary optimality conditions for optimal control problems governed by steady, incompressible Navier-Stokes equations with shear-dependent viscosity. The main difficulty derives from the fact that equations of this type may exhibit non-uniqueness of weak solutions, and is overcome by introducing a family of approximate control problems governed by well posed generalized Stokes systems and by passing to the limit in the corresponding optimality...