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Issue ESAIM: Proc.
Volume 17, 2007
CSVAA 2004 - Control Set-Valued Analysis and Applications
Page(s) 143 - 166
DOI http://dx.doi.org/10.1051/proc:071709
Published online 26 April 2007

ESAIM: Proc., April 2007, Vol. 17, pp. 143-166
DOI: 10.1051/proc:071709

Discriminating distributed sentinel involving a Navier-Stokes problem and parameter identification

Jean Velin

Université des Antilles et de La Guyane, Campus Fouillole 97159 Pointe-à-Pitre


(Published online: 26 April 2007)

Abstract
In this paper, we consider a Navier-Stokes system with missing initial data condition and perturbation distributed term or pollution term. We show that a discriminating distributed Sentinel with constraints can be associated to this system and allows to characterize this pollution. Our major result is based on an adapted distributed Carleman Inequality permitting to revisit a study investigated by Lions in [15].


Résumé
Dans ce papier, nous considérons un système de Navier-Stokes pour lequel au terme source est ajouté un terme de pollution et à la donnée initiale est affectée une incertitude ou terme manquant. Nous montrons qu'une Sentinelle distribuée, discriminante avec contraintes peut-être associée à ce système et permet alors de caractériser cette pollution. Notre principale résultat est basé sur une inégalité de Carleman adaptée. Ainsi, nous revoyons une étude abordée par Lions dans [15].


Mathematics Subject Classification. 93B05, 93C20, 49K20, 35K20

Key words: Navier-Stokes system, Sentinel, null-controllability, Carleman inequalities


© EDP Sciences, ESAIM 2007


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