Physical space approach to wave equation bilinear estimates revisit

2023/03/23 by Wang, Sheng, Zhou, Yi · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2303.13081

openalex publication_date 2023/03/23 · openalex created_date 2023/03/25 · openalex updated_date 2026/07/28

Abstract

In the paper by Klainerman, Rodnianski and Tao \citeKlainerman-Rodnianski-Tao, they give a physical space proof to a classical result of Klainerman and Machedon \citeKlainerman-Machedon for the bilinear space-time estimates of null forms. In this paper, we shall give an alternative and very simple physical space proof of the same bilinear estimates by applying div-curl type lemma of Zhou \citeZhou and Wang-Zhou \citeWang-Zhou-1, \citeWang-Zhou-2. As far as we known, the later development of wave maps \citeSterbenz-1, \citeSterbenz-2, \citeTao-1, \citeTao-2, \citeTataru-1, \citeTataru-2, and the proof of bounded curvature conjecture \citeKlainerman-Rodnianski-Szeftel-1, \citeKlainerman-Rodnianski-Szeftel-2 rely on basic idea of Klainerman and Machedon \citeKlainerman-Machedon as well as Klainerman, Rodnianski and Tao \citeKlainerman-Rodnianski-Tao.

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• Spinorial Div-Curl Structure and Bilinear Null-Form Estimates for Dirac Equations

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