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 a subdomain . The result that we obtained in this paper is as follows. Suppose that is a given solution of the Navier-Stokes equations. Let be a given initial condition and where is small enough. Then there exists a locally distributed control such that the solution of the Navier-Stokes equations:
On étudie le problème de contrôlabilité locale exacte pour les équations de Navier-Stokes incompressibles dans un domaine borné avec un contrôle réparti dans un sous-domaine On obtient le résultat suivant. Supposons que soit une solution des équations de Navier-Stokes et une condition initiale telle que pour assez petit. On montre alors qu’il existe un contrôle localement réparti tel que la solution des équations de Navier-Stokes :
Keywords: locally distributed control, Navier-Stokes system
@article{COCV_2001__6__39_0, author = {Imanuvilov, Oleg Yu.}, title = {Remarks on exact controllability for the {Navier-Stokes} equations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {39--72}, publisher = {EDP-Sciences}, volume = {6}, year = {2001}, mrnumber = {1804497}, zbl = {0961.35104}, language = {en}, url = {http://www.numdam.org/item/COCV_2001__6__39_0/} }
TY - JOUR AU - Imanuvilov, Oleg Yu. TI - Remarks on exact controllability for the Navier-Stokes equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2001 SP - 39 EP - 72 VL - 6 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_2001__6__39_0/ LA - en ID - COCV_2001__6__39_0 ER -
Imanuvilov, Oleg Yu. Remarks on exact controllability for the Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 6 (2001), pp. 39-72. http://www.numdam.org/item/COCV_2001__6__39_0/
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