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

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.


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


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