E. Fernandez-cara, S. Guerrero, and O. Yu, ´ etant donnés deuxélémentsdeuxéléments distincts y 0 et y 1 de l'espace desétatsdesétats et un temps arbitraire T , il existe une trajectoire du système qui partàpartà l'instant initial de y 0 et arrive au temps T en y 1 " . Cependant, il est naturel de s'interroger sur la contrôlabilité locale exacte aux trajectoires d'un système de Navier-Stokes. Cette question a fait l'objet de diversesétudesdiversesétudes, Résultats antérieurs Du fait du caractère dissipatif et non réversible deséquationsdeséquations de Navier-Stokes on ne peut Imanuvilov et J.-P. Puel o` u la contrôlabilité exacte locale aux trajectoires estétablieestétablie dans le cas de conditions au bord du type Dirichlet

O. Fursikov and . Yu, Imanuvilov et [45] de S. Guerrero o` u un résultat similaire est obtenu dans le cadre de conditions au bord de type Navier rappelées ci-dessous dans (4.8). La différence majeure entre ces articles provient des conditions demandées sur lesétatsàlesétatslesétatsà atteindre

. Dans, Coron et S. Guerrero obtiennent la contrôlabilité localè a zéro d'un système de Navier-Stokes 2-D sur un

. Dans, Coron montre la contrôlabilité globale approchée d'un système de NS 2-D avec conditions de Navier en utilisant la méthode du retour et en conjugant ce résultat avec un résultat local, J.-M. Coron et A. V. Fursikov

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