A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions |
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| Authors: | Jun Kato Makoto Nakamura Tohru Ozawa |
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| Institution: | 1. JSPS Research Fellow, Department of Mathematics, Kyoto University, Kyoto 606‐8502, Japan;2. Mathematical Institute, Tohoku University, Sendai 980‐8578, Japan;3. Department of Mathematics, Hokkaido University, Sapporo 060‐0810, Japan |
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| 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. © 2006 Wiley Periodicals, Inc. |
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