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

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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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Official URL: http://www.sciencedirect.com/science/article/pii/S0021782497899564


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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
Deposited On:04 Jul 2012 10:06
Last Modified:12 Dec 2018 15:08

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