Global solutions for 3D quadratic Schrödinger equations

Pierre Germain, Nader Masmoudi, Jalal Shatah

Research output: Contribution to journalArticlepeer-review


This is the first of the three papers where we present a new method based on the concept of space-time resonance to prove global existence of small solutions to nonlinear dispersive equations. The idea is that time resonances (dynamical systems resonances) correspond to interactions between plane waves; but since for dispersive equations we deal with localized solutions, it is crucial to take also into account the traveling speeds of the different wave packets. Here we show how this idea, and the analytical method that this naturally suggests, leads to a simple proof of global existence and scattering for quadratic nonlinear Schrödinger equations in three dimensions.

Original languageEnglish (US)
Pages (from-to)414-432
Number of pages19
JournalInternational Mathematics Research Notices
Issue number3
StatePublished - 2009

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Global solutions for 3D quadratic Schrödinger equations'. Together they form a unique fingerprint.

Cite this