Global existence results for nonlinear Schrödinger equations with quadratic potentials
Rémi Carles - MAB, UMR CNRS 5466 and Université Bordeaux 1, 351 cours de la Libération, F-33 405 Talence cedex, France (email)
Abstract: 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.
Keywords: Nonlinear Schrödinger equation, Mehler's formula, Strichartz estimates, global well-posedness, scattering.
Received: June 2004; Revised: February 2005; Available Online: April 2005.
2015 Impact Factor1.127