Uniform local null control of the Leray-α model

This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null...

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Detalles Bibliográficos
Autores: Dias Araruna, Fágner, Fernández Cara, Enrique, Araujo de Souza, Diego
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2014
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/41441
Acceso en línea:http://hdl.handle.net/11441/41441
https://doi.org/10.1051/cocv/2014011
Access Level:acceso abierto
Palabra clave:Null controllability
Carleman inequalities
Leray-α model
Navier−Stokes equations
Descripción
Sumario:This paper deals with the distributed and boundary controllability of the so called Leray-α model. This is a regularized variant of the Navier−Stokes system (α is a small positive parameter) that can also be viewed as a model for turbulent flows. We prove that the Leray-α equations are locally null controllable, with controls bounded independently of α. We also prove that, if the initial data are sufficiently small, the controls converge as α → 0+ to a null control of the Navier−Stokes equations. We also discuss some other related questions, such as global null controllability, local and global exact controllability to the trajectories, etc.