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Conformal conservation law, time decay and scattering for nonlinear wave equations

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Abstract

We study the implications of the conformal conservation law for the time decay of solutions of nonlinear wave equations and present some improvements over previous work of Ginibre and Velo. We also consider the theory of nonlinear scattering and prove asymptotic completeness in a weighted Sobolev space.

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Author notes

  1. Kunio Hidano

    Present address: Department of Mathematics Faculty of Education, Mie University, 1515 Kamihama, 514-8507, Tsu Mie Prefecture, Japan

Authors and Affiliations

  1. Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, 192-0397, Tokyo, Japan

    Kunio Hidano

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  1. Kunio Hidano
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Hidano, K. Conformal conservation law, time decay and scattering for nonlinear wave equations. J. Anal. Math. 91, 269–295 (2003). https://doi.org/10.1007/BF02788791

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  • DOI: https://doi.org/10.1007/BF02788791

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