Space-Time resonances and the null condition for (first order) systems   of wave equations
  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. 
Fabio Pusateri and Jalal Shatah
math.AP