A new proof of long-range scattering for critical nonlinear Schrödinger equations

Jun Kato, Fabio Giuseppe Pusateri

Research output: Contribution to journalArticle

36 Scopus citations

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 languageEnglish (US)
Pages (from-to)923-940
Number of pages18
JournalDifferential and Integral Equations
Volume24
Issue number9-10
StatePublished - Sep 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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