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Global existence results for nonlinear Schrödinger equations with quadratic potentials

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  • 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.
    Mathematics Subject Classification: Primary: 35Q55; Secondary: 35A05, 35B30, 35B35.

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