%0 Journal Article
%T Morawetz estimates for the wave equation at low frequency
%A Andr¨¢s Vasy
%A Jared Wunsch
%J Mathematics
%D 2010
%I arXiv
%X We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low frequencies, independent of the geometry of the compact part of the manifold. We further prove a new type of Morawetz estimate in this context, with both hypotheses and conclusion localized inside the forward light cone. This result allows us to gain a 1/2 power of $t$ decay relative to what would be dictated by energy estimates, in a small part of spacetime.
%U http://arxiv.org/abs/1011.0906v2