A generalization of the weighted strichartz estimates for wave equations and an application to self-similar solutions

Jun Kato, Makoto Nakamura, Tohru Ozawa

研究成果: Article査読

12 被引用数 (Scopus)

抄録

Weighted Strichartz estimates with homogeneous weights with critical exponents are proved for the wave equation without a support restriction on the forcing term. The method of proof is based on expansion by spherical harmonics and on the Sobolev space over the unit sphere, by which the required estimates are reduced to the radial case. As an application of the weighted Strichartz estimates, the existence and uniqueness of self-similar solutions to nonlinear wave equations are proved on up to five space dimensions.

本文言語English
ページ(範囲)164-186
ページ数23
ジャーナルCommunications on Pure and Applied Mathematics
60
2
DOI
出版ステータスPublished - 2007 2
外部発表はい

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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