Asymptotics of radiation fields in asymptotically minkowski space

Dean Baskin, András Vasy, Jared Wunsch

Research output: Contribution to journalArticle

20 Scopus citations

Abstract

We consider a non-trapping n-dimensional Lorentzian manifold endowed with an end structure modeled on the radial compactification of Minkowski space. We find a full asymptotic expansion for tempered forward solutions of the wave equation in all asymptotic regimes. The rates of decay seen in the asymptotic expansion are related to the resonances of a natural asymptotically hyperbolic problem on the “northern cap” of the compactification. For small perturbations of Minkowski space that fit into our framework, our asymptotic expansions yield a rate of decay that improves on the Klainerman-Sobolev estimates.

Original languageEnglish (US)
Pages (from-to)1293-1364
Number of pages72
JournalAmerican Journal of Mathematics
Volume137
Issue number5
DOIs
StatePublished - Oct 1 2015

ASJC Scopus subject areas

  • Mathematics(all)

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