Geodesic
Controllability of three-dimensional Navier–Stokes equations and applications
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 6, 7 p.

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We formulate two results on controllability properties of the 3D Navier–Stokes (NS) system. They concern the approximate controllability and exact controllability in finite-dimensional projections of the problem in question. As a consequence, we obtain the existence of a strong solution of the Cauchy problem for the 3D NS system with an arbitrary initial function and a large class of right-hand sides. We also discuss some qualitative properties of admissible weak solutions for randomly forced NS equations.

Classification : 35Q30, 60H15, 76D05, 93B05, 93C20
Keywords: Approximate controllability, exact controllability in projections, 3D Navier–Stokes system, Agrachev–Sarychev method, stationary solutions, irreducibility. 
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     title = {Controllability of three-dimensional {Navier{\textendash}Stokes} equations and applications},
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Shirikyan, Armen. Controllability of three-dimensional Navier–Stokes equations and applications. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2005-2006), Exposé no. 6, 7 p. http://geodesic.mathdoc.fr/item/SEDP_2005-2006____A6_0/

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