Displaying similar documents to “Uniqueness results for stokes equations and their consequences in linear and nonlinear control problems”

Remarks on exact controllability for the Navier-Stokes equations

Oleg Yu. Imanuvilov (2001)

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 Ω with control distributed in a subdomain ω ⊂ Ω ⊂ ℝ n , n ∈ { 2 , 3 } . The result that we obtained in this paper is as follows. Suppose that v ^ ( t , x ) is a given solution of the Navier-Stokes equations. Let v 0 ( x ) be a given initial condition and ∥ v ^ ( 0 , · ) - v 0 ∥ < ε where ε is small enough. Then there exists a locally distributed control u , supp u ⊂ ( 0 , T ) × ω such that the solution v ( t , x ) of the Navier-Stokes equations: ...