Global existence of low regularity solutions of nonlinear wave equations (Q1895766)

We prove a global existence theorem for small data solutions to nonlinear wave equations with null condition type nonlinearities under weak regularity assumptions. The proof consists of applying the conformal compactification method and establishing estimates of Klainerman-Machedon type for solutions of the wave equation on the Einstein cylinder manifold. This is accomplished by estimating some Fourier integral operators arising from the parametrix representation of the solutions.