Weighted Strichartz estimates for the wave equation in even space dimensions

Jun Kato, Tohru Ozawa

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We prove the weighted Strichartz estimates for the wave equation in even space dimensions with radial symmetry in space. Although the odd space dimensional cases have been treated in our previous paper [5], the lack of the Huygens principle prevents us from a similar treatment in even space dimensions. The proof is based on the two explicit representations of solutions due to Rammaha [11] and Takamura [14] and to Kubo-Kubota [6]. As in the odd space dimensional cases [5], we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.

Original languageEnglish
Pages (from-to)747-764
Number of pages18
JournalMathematische Zeitschrift
Volume247
Issue number4
DOIs
Publication statusPublished - 2004 Aug
Externally publishedYes

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Strichartz Estimates
Weighted Estimates
Wave equation
Odd
Huygens' Principle
Radial Symmetry
Semilinear Wave Equation
Self-similar Solutions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Weighted Strichartz estimates for the wave equation in even space dimensions. / Kato, Jun; Ozawa, Tohru.

In: Mathematische Zeitschrift, Vol. 247, No. 4, 08.2004, p. 747-764.

Research output: Contribution to journalArticle

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