Space-Time resonances and the null condition for (first order) systems of wave equations

Abstract

In this manuscript we prove global existence and linear asymptotic behavior of small solutions to nonlinear wave equations. We assume that the quadratic part of the nonlinearity satisfies a non-resonant condition which is a generalization of the null condition given by Klainerman.

v2: Revised introduction and presentation. Extended bibliography

References in corpus (3)

• Global existence for the Einstein vacuum equations in wave coordinates
• Global solutions for 2D quadratic Schrodinger equations
• Global existence for coupled Klein-Gordon equations with different speeds