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A generalization of the weighted Strichartz estimates for wave equations and an application to self‐similar solutions
Author(s) -
Kato Jun,
Nakamura Makoto,
Ozawa Tohru
Publication year - 2007
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20133
Subject(s) - mathematics , uniqueness , sobolev space , mathematical analysis , wave equation , nonlinear system , forcing (mathematics) , spherical harmonics , space (punctuation) , unit sphere , generalization , linguistics , philosophy , physics , quantum mechanics
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.