Morawetz estimates for the wave equation at low frequency

András Vasy, Jared Wunsch*

*Corresponding author for this work

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1221-1254
Number of pages34
JournalMathematische Annalen
Volume355
Issue number4
DOIs
StatePublished - Jan 1 2013

ASJC Scopus subject areas

  • Mathematics(all)

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