Some controllability results for the N-Dimensional Navier-Stokes and Boussinesq systems with N-1 scalar controls

In this paper we deal with some controllability problems for systems of the Navier-Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N-dimensional systems (N + 1 scalar unknowns in the case of the Navier–Stokes equations) with N − 1 scalar contr...

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Detalles Bibliográficos
Autores: Fernández Cara, Enrique, Guerrero Rodríguez, Sergio, Imanuvilov, Oleg Yu, Puel, Jean-Pierre
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2006
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41449
Acceso en línea:http://hdl.handle.net/11441/41449
https://doi.org/10.1137/04061965X
Access Level:acceso abierto
Palabra clave:Navier–Stokes system
exact controllability
Carleman inequalities
Descripción
Sumario:In this paper we deal with some controllability problems for systems of the Navier-Stokes and Boussinesq kind with distributed controls supported in small sets. Our main aim is to control N-dimensional systems (N + 1 scalar unknowns in the case of the Navier–Stokes equations) with N − 1 scalar control functions. In a first step, we present some global Carleman estimates for suitable adjoint problems of linearized Navier–Stokes and Boussinesq systems. In this way, we obtain null controllability properties for these systems. Then, we deduce results concerning the local exact controllability to the trajectories. We also present (global) null controllability results for some (truncated) approximations of the Navier–Stokes equations.