Global existence results for nonlinear Schrodinger equations with quadratic potentials
Analysis of PDEs
2007-05-23 v2
Abstract
We prove that no finite time blow up can occur for nonlinear Schroedinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of the linear equation, which makes it possible to use continuity arguments and to control the nonlinear effects.
Cite
@article{arxiv.math/0405197,
title = {Global existence results for nonlinear Schrodinger equations with quadratic potentials},
author = {Remi Carles},
journal= {arXiv preprint arXiv:math/0405197},
year = {2007}
}
Comments
Some typos fixed, Proposition 1.1 extended. Final version to appear in DCDS