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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 an extended...
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...
In this paper, we consider the well-known Fattorini’s criterion for approximate controllability of infinite dimensional linear systems of type ′ = + . We precise the result proved by Fattorini in [H.O. Fattorini, 4 (1966) 686–694.] for bounded input , in the case where can be unbounded or in the case of finite-dimensional controls. More precisely, we prove that if Fattorini’s criterion is satisfied and if the set of geometric multiplicities of is bounded then approximate controllability can be...
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