In this note we describe a recent result obtained by the author and Shatah  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 .
|Original language||English (US)|
|Number of pages||17|
|Journal||Bolletino dell Unione Matematica Italiana|
|State||Published - Jan 1 2013|
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