Sur le comportement des solutions d’équations de Schrödinger non linéaires à croissance exponentielle

Bahouri, Hajer

Séminaire Laurent Schwartz — EDP et applications (2014-2015), Exposé no. 10, 11 p.

On se propose dans cet exposé de décrire le comportement des solutions de l’équation de Schrödinger non linéaire à croissance exponentielle, où la norme d’Orlicz joue un rôle crucial. Notre analyse qui est basée sur les décompositions en profils met en lumière le rôle distingué de la composante $\mathbf{1}$-oscillante de la suite des données initiales. Ce phénomène est complètement différent de ceux obtenus dans le cadre des équations semi-linéaires dispersives critiques, où toutes les composantes oscillantes créent le même effet non linéaire, à un changement d’échelle près.

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