Global existence of solutions to Schrödinger equations on compact riemannian manifolds below $H^1$

[Existence globale de solutions des équations de Schrödinger sur les variétés riemanniennes compactes en régularité plus faible que $H^1$]

Zhong, Sijia

Bulletin de la Société Mathématique de France, Tome 138 (2010), p. 583-613 / Harvested from Numdam

Résumé

Nous nous intéressons dans cet article au caractère bien posé des équations de Schrödinger non-linéaires cubiques défocalisantes sur les variétés riemanniennes compactes sans bord, en régularité $H^s$, $s<1$, sous certaines conditions bilinéaires de Strichartz. Nous trouvons un $\tilde{s}<1$ tel que la solution est globale pour $s>\tilde{s}$.

Abstract

In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. $s<1$, under some bilinear Strichartz assumption. We will find some $\tilde{s}<1$, such that the solution is global for $s>\tilde{s}$.

Détail

Publié le : 2010-01-01

MR 2794885 | Zbl 1236.35002

DOI : https://doi.org/10.24033/bsmf.2597
Classification:  35Q55,  37K05,  37L50,  81Q20
Mots clés: Équation de schrödinger, variété riemanienne compacte, globalité, I-méthode

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