Abstract
We present a new proof of global existence and long range scattering, from small initial data, for the one-dimensional cubic gauge invariant nonlinear Schrödinger equation, and for Hartree equations in dimension n ≥ 2. The proof relies on an analysis in Fourier space, related to the recent works of Germain, Masmoudi, and Shatah on space-time resonances. An interesting feature of our approach is that we are able to identify the long range phase correction term through a very natural stationary phase argument.
Original language | English (US) |
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Pages (from-to) | 923-940 |
Number of pages | 18 |
Journal | Differential and Integral Equations |
Volume | 24 |
Issue number | 9-10 |
State | Published - Sep 2011 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics