Long time existence for semilinear wave equations on asymptotically flat space-times

Chengbo Wang

Published 2015-04-22Version 1

We study the long time existence of solutions to some semilinear wave equations of the form $\Box u=|u|^p$ with compactly supported small data, on a large class of (1+n)-dimensional nonstationary asymptotically flat backgrounds, which models the black hole space-times. Under the assumption that uniform energy bounds and a weak form of local energy estimates hold forward in time, we give a lower bound of the lifespan when n=3 and p is less than the critical one, which is sharp in general. For the critical case with n=3, 4, we get an exponential lower bound of the lifespan.