Stability results for the nonlinear Schrödinger equation on Diophantine tori
[Résultats de stabilité pour l’équation de Schrödinger non linéaire sur des tores diophantiens]
Nicolas Camps1
1 IRMAR - UMR CNRS 6625 Univ Rennes F-35000 Rennes FRANCE
Journées équations aux dérivées partielles (2024), Exposé no. 3, 15 p.

Nous présentons deux résultats de stabilité en temps long pour l’équation de Schrödinger non linéaire posée sur des tores diophantiens. Ce proceeding pour la conférence “Journées Équations aux dérivées partielles” offre l’occasion de présenter des méthodes modernes à l’interface des équations aux dérivées partielles (EDP) et de la mécanique classique, actuellement en cours de développement pour étudier la dynamique d’EDP hamiltoniennes résonantes.

We present two results of enhanced long-time stability for the nonlinear Schrödinger equation posed on rescaled tori with Diophantine properties. This proceeding for the conference “Journées Équations aux dérivées partielles” is the opportunity to give a glimpse on modern methods at the interface of PDEs and classical mechanics that are currently being developed to study the long-time dynamics of Hamiltonian resonant PDEs.

Publié le :
DOI : 10.5802/jedp.684
Classification : 35B34, 35B35, 35Q55, 37K45, 37K55
Nicolas Camps 1

1 IRMAR - UMR CNRS 6625 Univ Rennes F-35000 Rennes FRANCE 
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Nicolas Camps. Stability results for the nonlinear Schrödinger equation on Diophantine tori. Journées équations aux dérivées partielles (2024), Exposé no. 3, 15 p. doi : 10.5802/jedp.684. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.684/

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