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arXiv:math/0405197 [math.AP]AbstractReferencesReviewsResources

Global existence results for nonlinear Schrodinger equations with quadratic potentials

Remi Carles

Published 2004-05-11, updated 2005-02-18Version 2

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.

Comments: Some typos fixed, Proposition 1.1 extended. Final version to appear in DCDS
Journal: Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398
Categories: math.AP
Subjects: 35Q55, 35A05, 35B30, 35B35
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