2026-06-29T09:38:08Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/574052025-08-22T12:30:54Zcom_20.500.14352_14col_20.500.14352_15

Approximate controllability of the Stokes system on cylinders by external unidirectional forces Díaz Díaz, Jesús Ildefonso Fursikov, A.V. 517.977 cylindrical domain approximate controllability Stokes system Geometría diferencial 1204.04 Geometría Diferencial We 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. Ministerio de Ciencia e Innovación (España) Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T16:54:45Z 2023-06-20T16:54:45Z 1997 journal article https://hdl.handle.net/20.500.14352/57405 0021-7824 10.1016/S0021-7824(97)89956-4 spa PB 93/0443 restricted access application/pdf Elsevier