Controllability results for cascade systems of m coupled N -dimensional stokes and Navier-stokes systems by N – 1 scalar controls
In this paper we deal with the controllability properties of a system of m coupled Stokes systems or m coupled Navier-Stokes systems. We show the null-controllability of such systems in the case where the coupling is in a cascade form and when the control acts only on one of the systems. Moreover, w...
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| Published in | ESAIM. Control, optimisation and calculus of variations Vol. 29; p. 31 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
2023
|
| Online Access | Get full text |
| ISSN | 1292-8119 1262-3377 |
| DOI | 10.1051/cocv/2023014 |
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| Abstract | In this paper we deal with the controllability properties of a system of
m
coupled Stokes systems or
m
coupled Navier-Stokes systems. We show the null-controllability of such systems in the case where the coupling is in a cascade form and when the control acts only on one of the systems. Moreover, we impose that this control has a vanishing component so that we control a
m
×
N
state (corresponding to the velocities of the fluids) by
N
— 1 distributed scalar controls. The proof of the controllability of the coupled Stokes systems is based on a Carleman estimate for the adjoint system. The local null-controllability of the coupled Navier-Stokes systems is then obtained by means of the source term method and a Banach fixed point. |
|---|---|
| AbstractList | In this paper we deal with the controllability properties of a system of
m
coupled Stokes systems or
m
coupled Navier-Stokes systems. We show the null-controllability of such systems in the case where the coupling is in a cascade form and when the control acts only on one of the systems. Moreover, we impose that this control has a vanishing component so that we control a
m
×
N
state (corresponding to the velocities of the fluids) by
N
— 1 distributed scalar controls. The proof of the controllability of the coupled Stokes systems is based on a Carleman estimate for the adjoint system. The local null-controllability of the coupled Navier-Stokes systems is then obtained by means of the source term method and a Banach fixed point. |
| Author | Wu-Zhang, Yingying Takahashi, Takéo de Teresa, Luz |
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| Cites_doi | 10.1016/j.anihpc.2006.11.001 10.1007/s11401-008-0280-x 10.1007/s00030-018-0537-3 10.1137/04061965X 10.5802/ahl.45 10.1137/060653135 10.1007/s00222-014-0512-5 10.1016/j.matpur.2018.03.004 10.1007/s11587-016-0288-6 10.3934/mcrf.2011.1.267 10.1007/s00498-016-0182-5 10.1007/978-1-4612-5561-1 10.1016/j.matpur.2013.03.007 10.1007/978-3-0348-0551-3 10.1016/j.jde.2008.10.019 10.1016/j.jmaa.2016.06.058 10.1016/j.jde.2017.04.009 10.1016/j.matpur.2004.02.010 10.4171/PM/1859 10.1090/qam/510972 10.1016/j.jfa.2014.07.024 |
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| Snippet | In this paper we deal with the controllability properties of a system of
m
coupled Stokes systems or
m
coupled Navier-Stokes systems. We show the... |
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| Title | Controllability results for cascade systems of m coupled N -dimensional stokes and Navier-stokes systems by N – 1 scalar controls |
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