Space-time resonances and the null condition for wave equations

Fabio Giuseppe Pusateri

Research output: Contribution to journalArticle

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Abstract

In this note we describe a recent result obtained by the author and Shatah [26] concerning global existence and scattering for small solutions of nonlinear wave equations. Based on the analysis of space-time resonances, we formulate a very natural non-resonance condition for quadratic nonlinearities that guarantees the existence of global solutions with linear asymptotic behavior. This non-resonance condition turns out to be a generalization of the null condition given by Klainerman in his seminal work [21].

Original languageEnglish (US)
Pages (from-to)513-529
Number of pages17
JournalBolletino dell Unione Matematica Italiana
Volume6
Issue number3
StatePublished - Jan 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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