Controllability of three-dimensional Navier–Stokes equations and applications
Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Talk no. 6, 7 p.

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.
     author = {Shirikyan, Armen},
     title = {Controllability of three-dimensional Navier--Stokes equations and applications},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2005-2006},
     note = {talk:6},
     language = {en},
     url = {}
Shirikyan, Armen. Controllability of three-dimensional Navier–Stokes equations and applications. Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Talk no. 6, 7 p.

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