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Approximate controllability of the Stokes system on cylinders by external unidirectional forces

Díaz Díaz, Jesús Ildefonso and Fursikov, A.V. (1997) Approximate controllability of the Stokes system on cylinders by external unidirectional forces. Journal de Mathématiques Pures et Appliquées, 76 (4). pp. 353-375. ISSN 0021-7824

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Abstract

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.


Item Type:Article
Uncontrolled Keywords:cylindrical domain; approximate controllability; Stokes system
Subjects:Sciences > Mathematics > Differential geometry
ID Code:15822
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