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 , 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  and Takamura  and to Kubo-Kubota . As in the odd space dimensional cases , we are also able to construct self-similar solutions to semilinear wave equations on the basis of the weighted Strichartz estimates.
ASJC Scopus subject areas
- 数学 (全般)