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

Jun Kato, Makoto Nakamura, Tohru Ozawa

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)164-186
Number of pages23
JournalCommunications on Pure and Applied Mathematics
Volume60
Issue number2
DOIs
Publication statusPublished - 2007 Feb
Externally publishedYes

Fingerprint

Strichartz Estimates
Weighted Estimates
Self-similar Solutions
Wave equations
Wave equation
Sobolev spaces
Forcing Term
Spherical Harmonics
Nonlinear Wave Equation
Unit Sphere
Critical Exponents
Sobolev Spaces
Existence and Uniqueness
Restriction
Estimate
Generalization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A generalization of the weighted strichartz estimates for wave equations and an application to self-similar solutions. / Kato, Jun; Nakamura, Makoto; Ozawa, Tohru.

In: Communications on Pure and Applied Mathematics, Vol. 60, No. 2, 02.2007, p. 164-186.

Research output: Contribution to journalArticle

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