Geodesic
Approximate controllability of the~Navier--Stokes system in unbounded domains
Sbornik. Mathematics, Tome 194 (2003) no. 11, pp. 1725-1745

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The question of the approximate controllability for the 2- and the 3-dimensional Navier–Stokes system defined in the exterior of a bounded domain $\omega$ 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. 
@article{SM_2003_194_11_a6,
     author = {P. O. Shorygin},
     title = {Approximate controllability of {the~Navier--Stokes} system in unbounded domains},
     journal = {Sbornik. Mathematics},
     pages = {1725--1745},
     publisher = {mathdoc},
     volume = {194},
     number = {11},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_11_a6/}
}
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P. O. Shorygin. Approximate controllability of the~Navier--Stokes system in unbounded domains. Sbornik. Mathematics, Tome 194 (2003) no. 11, pp. 1725-1745. http://geodesic.mathdoc.fr/item/SM_2003_194_11_a6/