Geodesic
Stabilizing a~solution of the 2D Navier-Stokes system in the exterior of a~bounded domain by means of a~control on the boundary
Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1244-1268

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The problem of stabilizing a solution of the 2D Navier-Stokes system defined in the exterior of a bounded domain with smooth boundary is investigated. For a given initial velocity field a control on the boundary of the domain must be constructed such that the solution stabilizes to a prescribed vortex solution or trivial solution at the rate of $1/{t^k}$. On the way, related questions are investigated, concerning the behaviour of the spectrum of an operator under a relatively compact perturbation and the existence of attracting invariant manifolds. Bibliography: 21 titles.
Keywords: Navier-Stokes system, Lamb-Oseen vortex, stabilization, boundary control, invariant manifolds. 
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     author = {A. V. Gorshkov},
     title = {Stabilizing a~solution of the {2D} {Navier-Stokes} system in the exterior of a~bounded domain by means of a~control on the boundary},
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A. V. Gorshkov. Stabilizing a~solution of the 2D Navier-Stokes system in the exterior of a~bounded domain by means of a~control on the boundary. Sbornik. Mathematics, Tome 203 (2012) no. 9, pp. 1244-1268. http://geodesic.mathdoc.fr/item/SM_2012_203_9_a1/