# American Institute of Mathematical Sciences

February  2005, 13(2): 385-398. doi: 10.3934/dcds.2005.13.385

## Global existence results for nonlinear Schrödinger equations with quadratic potentials

 1 MAB, UMR CNRS 5466 and Université Bordeaux 1, 351 cours de la Libération, F-33 405 Talence cedex, France

Received  June 2004 Revised  February 2005 Published  April 2005

We prove that no finite time blow up can occur for nonlinear Schrödinger 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 control the nonlinear effects.
Citation: Rémi Carles. Global existence results for nonlinear Schrödinger equations with quadratic potentials. Discrete & Continuous Dynamical Systems - A, 2005, 13 (2) : 385-398. doi: 10.3934/dcds.2005.13.385
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