Space-Time Resonances and the Null Condition for Wave Equations
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...