A physical space approach to wave equation bilinear estimates

Details A physical space approach to wave equation bilinear estimates A physical space approach to wave equation bilinear estimates

2001-06-12

arxiv.org/abs/math/0106091v2

Mathematics

Analysis of PDEs

33 pages, no figures, submitted to Journal d'Analyse Jerusalem. Some minor typos corrected, and some additional remarks made f

Scientific paper

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 with connections with non-zero curvature). In this note we give some techniques to prove these estimates which rely more on physical space methods such as vector fields, tube localization, splitting into coarse and fine scales, and induction on scales (in the spirit of recent papers of Wolff).

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