Global existence results for nonlinear Schrodinger equations with quadratic potentials

Details Global existence results for nonlinear Schrodinger equations with quadratic potentials Global existence results for nonlinear Schrodinger equations with quadratic potentials

2004-05-11

arxiv.org/abs/math/0405197v2

Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398

Mathematics

Analysis of PDEs

Some typos fixed, Proposition 1.1 extended. Final version to appear in DCDS

Scientific paper

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.

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