Global existence results for nonlinear Schrodinger equations with quadratic potentials

Remi Carles

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Global existence results for nonlinear Schrodinger equations with quadratic potentials

Remi Carles

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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.

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Remi Carles. 2005-02-18. Global existence results for nonlinear Schrodinger equations with quadratic potentials. https://arxiv.org/abs/math/0405197

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