A physical space approach to wave equation bilinear estimates

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Abstract

Bilinear estimates for the wave equation in Minkowski space are normally proven using the Fourier transform and Plancherel's theorem. However, such methods are difficult to carry over to non-flat situations (such as wave equations with rough metrics or connections with non-zero curvature). In this note, we describe an alternative physical space approach which relies on vector fields, energy estimates as well as tube localization, splitting into coarse and fine scales, and induction on scales (in the spirit of Wolff [29], [30]).

Original languageEnglish (US)
Article numberBF02868479
Pages (from-to)299-336
Number of pages38
JournalJournal d'Analyse Mathematique
Volume87
Issue number1
DOIs
StatePublished - Jan 1 2002

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics(all)

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