%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Fursikov, A.V.
%T Approximate controllability of the Stokes system on cylinders by external unidirectional forces
%D 1997
%@ 0021-7824
%U https://hdl.handle.net/20.500.14352/57405
%X Wt,give some negative and positive results on the approximate controllability of the Stokes system formulated on a cylinder Omega = G x R of R-3 when the control is a density of external unidirectional forces. We distinguish the case where the direction of the controls e is parallel to the cylinder generatrix (e = e(3)) from the one where e is orthogonal to this generatrix (e = e(1)). A negative result in the case of e = e(3) is proved for periodic boundary conditions on x(3), and homogeneous Dirichlet conditions on partial derivative G x R where G is a general set of R-2. In contrast to that, the approximate controllability is proved for homogeneous Dirichlet conditions on partial derivative Omega (i.e. zero on partial derivative G x R and solutions in (L-2(G x R))(3) for any t), when G is a rectangle and e = e(1) is orthogonal to the cylinder generatrix.
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