Physical space approach to wave equation bilinear estimates revisit
Abstract
In the paper by Klainerman, Rodnianski and Tao Klainerman-Rodnianski-Tao, they give a physical space proof to a classical result of Klainerman and Machedon Klainerman-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 Zhou and Wang-Zhou Wang-Zhou-1, Wang-Zhou-2. As far as we known, the later development of wave maps Sterbenz-1, Sterbenz-2, Tao-1, Tao-2, Tataru-1, Tataru-2, and the proof of bounded curvature conjecture Klainerman-Rodnianski-Szeftel-1, Klainerman-Rodnianski-Szeftel-2 rely on basic idea of Klainerman and Machedon Klainerman-Machedon as well as Klainerman, Rodnianski and Tao Klainerman-Rodnianski-Tao.
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