Space-time resonances

2011/02/08 by Pierre Germain, Germain, Pierre · 1 citation
Mathematics · #35A01 37L50 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35A01 #msc:37L50

paper · pdf · doi:10.48550/arxiv.1102.1695

10 pages

arxiv created 2011/02/08 · arxiv updated 2011/02/09

Abstract

This article is a short exposition of the space-time resonances method. It was introduced by Masmoudi, Shatah, and the author, in order to understand global existence for nonlinear dispersive equations, set in the whole space, and with small data. The idea is to combine the classical concept of resonances, with the feature of dispersive equations: wave packets propagate at a group velocity which depends on their frequency localization. The analytical method which follows from this idea turns out to be a very general tool.

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