Dept. Math, Hokkaido Univ. EPrints Server

Weighted Strichartz estimates for the wave equation in even space dimensions

Preprint Series # 603
Kato, Jun and Ozawa, Tohru Weighted Strichartz estimates for the wave equation in even space dimensions. (2003);

[img]PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
188Kb

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 [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.

Item Type:Preprint
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:10