Article Contents
Article Contents

# Global existence results for nonlinear Schrödinger equations with quadratic potentials

• 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.

 Citation: