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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 the Navier-Stokes equations coincides
with this stationary point.
Imanuvilov, O. Yu.. "On exact controllability for the Navier-Stokes equations." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 97-131. <http://eudml.org/doc/197299>.
@article{Imanuvilov2010, abstract = {
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.
}, author = {Imanuvilov, O. Yu.}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, keywords = {Locally distributed control; Navier-Stokes equations.; locally distributed control}, language = {eng}, month = {3}, pages = {97-131}, publisher = {EDP Sciences}, title = {On exact controllability for the Navier-Stokes equations}, url = {http://eudml.org/doc/197299}, volume = {3}, year = {2010}, }
TY - JOUR AU - Imanuvilov, O. Yu. TI - On exact controllability for the Navier-Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations DA - 2010/3// PB - EDP Sciences VL - 3 SP - 97 EP - 131 AB -
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.
LA - eng KW - Locally distributed control; Navier-Stokes equations.; locally distributed control UR - http://eudml.org/doc/197299 ER -