Dynamics of Partial Differential Equations

Volume 10 (2013)

Number 2

Almost global existence for a fractional Schrödinger equation on spheres and tori

Pages: 171 – 176

DOI: https://dx.doi.org/10.4310/DPDE.2013.v10.n2.a3

Authors

Dario Bambusi (Dipartimento di Matematica, Università degli studi di Milano, Italy)

Yannick Sire (Centre de Mathématique et Informatique Laboratoire d’Analyse, Topologie, Probabilité (LATP), Université Aix-Marseille, France)

Abstract

We study the time of existence of the solutions of the following Schrödinger equation$$i\psi_t = (-\Delta)^s \psi +f(|\psi|^2)\psi,\,\,\, x \in \mathbb{S^d}\ ,\ or\ x\in\mathbb{T}^d$$where $(-\Delta)^s$ stands for the spectrally defined fractional Laplacian with $s>1/2$ and $f$ a smooth function. We prove an almost global existence result for almost all $s>1/2$.

Keywords

almost global existence, fractional Schr¨odinger equation

2010 Mathematics Subject Classification

35-xx

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Published 4 June 2013