A generalization of the weighted Strichartz estimates for wave equations large and an application to self-similar solutions

Abstract

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.