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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]).

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Authors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Sergiu Klainerman & Igor Rodnianski

  2. Department of Mathematics, UCLA, 90095-1555, Los Angeles, CA, USA

    Terence Tao

Authors
  1. Sergiu Klainerman
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  2. Igor Rodnianski
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  3. Terence Tao
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Correspondence to Sergiu Klainerman.

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Klainerman, S., Rodnianski, I. & Tao, T. A physical space approach to wave equation bilinear estimates. J. Anal. Math. 87, 299–336 (2002). https://doi.org/10.1007/BF02868479

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  • DOI: https://doi.org/10.1007/BF02868479

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