A generalization of the weighted Strichartz estimates for wave equations large and an application to self-similar solutions
Preprint Series # 708
Kato, Jun and Nakamura, Makoto and Ozawa, Tohru A generalization of the weighted Strichartz estimates for wave equations large and an application to self-similar solutions. (2005);
Weighted Strichartz estimates with homogeneous weights with
critical exponents are proved for the wave equation without
support restriction on the forcing term.
The method of proof is based on the 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
is proved up to 5 space dimensions.