Global solutions for 3D quadratic Schrödinger equations

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Abstract

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
Volume2009
Issue number3
DOIs
Publication statusPublished - 2009

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ASJC Scopus subject areas

  • Mathematics(all)

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