A physical space approach to wave equation bilinear estimates |
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Authors: | Sergiu Klainerman Igor Rodnianski Terence Tao |
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Affiliation: | (1) Department of Mathematics, Princeton University, 08544 Princeton, NJ, USA;(2) Department of Mathematics, UCLA, 90095-1555 Los Angeles, CA, USA |
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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]). |
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