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Pusateri, Fabio:
Space-Time Resonances and the Null Condition for Wave Equations
Bollettino dell'Unione Matematica Italiana Serie 9 6 (2013), fasc. n.3, p. 513-529, (English)
pdf (317 Kb), djvu (167 Kb). | MR 3202837

Sunto

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].
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