Abstract:
The question of the approximate controllability for the 2- and
the 3-dimensional Navier–Stokes system defined in the exterior of
a bounded domain ω or in the entire space is studied. It is shown that one can find
boundary controls or locally distributed controls (having support in a prescribed bounded domain) defined on the right-hand side of the system such that in prescribed time the solution of the Navier–Stokes system becomes arbitrarily close to an arbitrary prescribed divergence-free vector field.
\Bibitem{Sho03}
\by P.~O.~Shorygin
\paper Approximate controllability of the~Navier--Stokes system in unbounded domains
\jour Sb. Math.
\yr 2003
\vol 194
\issue 11
\pages 1725--1745
\mathnet{http://mi.mathnet.ru/eng/sm784}
\crossref{https://doi.org/10.1070/SM2003v194n11ABEH000784}
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Linking options:
https://www.mathnet.ru/eng/sm784
https://doi.org/10.1070/SM2003v194n11ABEH000784
https://www.mathnet.ru/eng/sm/v194/i11/p141
This publication is cited in the following 3 articles:
Tujin Kim, Daomin Cao, “Local Exact Controllability of the Navier–Stokes Equations with the Condition on the Pressure on Parts of the Boundary”, SIAM J Control Optim, 48:6 (2010), 3805
A. V. Fursikov, “Flow of a viscous incompressible fluid around a body: boundary-value problems and minimization of the work of a fluid”, Journal of Mathematical Sciences, 180:6 (2012), 763–816
Fursikov A.V., Gunzburger M.D., Hou L.S., “Optimal boundary control for the evolutionary Navier–Stokes system: The three-dimensional case”, SIAM J. Control Optim., 43:6 (2005), 2191–2232
Citation in format AMSBIB
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