Almost global existence for some semilinear wave equations

Abstract

We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave equations, as opposed to the much harder to prove 1/t decay.

To appear in Journal d'Analyse. A paper on the quasilinear case will follow