On exact controllability for the Navier-Stokes equations. (English) Zbl 1052.93502

Imanuvilov, O. Yu.

ESAIM, Control Optim. Calc. Var. 3, 97-131 (1998).

Summary: 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 the Navier-Stokes equations coincides with this stationary point.

MSC:

93B05	Controllability
93C20	Control/observation systems governed by partial differential equations
35Q30	Navier-Stokes equations
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

locally distributed control

References:

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