Contrôlabilité de quelques équations cinétiques collisionnelles et non collisionnelles : Fokker-Planck et Vlasov-Navier-Stokes

Moyano, Iván

Séminaire Laurent Schwartz — EDP et applications (2016-2017), Exposé no. 5, 22 p.

Dans cet exposé nous présentons quelques résultats de contrôle pour les équations cinétiques. En particulier, nous nous concentrons sur deux modèles importants provenant de la littérature physique : l’équation de Fokker-Planck et le système de Vlasov-Navier-Stokes. Nous présentons les résultats obtenus dans le premier cas, de nature hypoellitique, dans [41], grâce à l’utilisation d’une inégalité spectrale pour le laplacien dans tout l’espace. Dans le cas non-collisionnel, nous présentons les résultats obtenus dans [50, 51] grâce à l’utilisation de la méthode du retour.

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