open access

https://doi.org/10.14943/83748

https://hdl.handle.net/2115/69352

Weighted Strichartz estimates for the wave equation in even space dimensions

英語

2003

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

603

1-20

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 [4], 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 [10] and Takamura [13] and to Kubo-Kubota [5]. As in the odd space dimensional cases [4], we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.

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