A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions
A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions
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DOI：
10.1002/cpa.20133
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发表时间：
2007-02
影响因子：
3
通讯作者：
J. Kato;Makoto Nakamura;T. Ozawa
中科院分区：
文献类型：
--
作者：
J. Kato;Makoto Nakamura;T. Ozawa
证明了具有临界指数的齐次权值的波动方程的加权Strichartz估计。证明方法是基于球面谐波展开和单位球面上的Sobolev空间，通过该空间，所需的估计被简化为径向情况。作为加权Strichartz估计的一个应用，证明了非线性波动方程自相似解在5维空间上的存在唯一性。©2006 Wiley期刊公司
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.