Almost global existence for cubic nonlinear Schrödinger equations in one space dimension

Jason Murphy, Fabio Pusateri

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We consider non-gauge-invariant cubic nonlinear Schrödinger equations in one space dimension. We show that initial data of size ϵ in a weighted Sobolev space lead to solutions with sharp Lx decay up to time exp(Cϵ-2). We also exhibit norm growth beyond this time for a specific choice of nonlinearity.

Original languageEnglish (US)
Pages (from-to)2077-2102
Number of pages26
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume37
Issue number4
DOIs
StatePublished - Apr 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Almost global existence
  • Cubic NLS
  • Method of space-time resonances

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