2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171161In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrödinger equation in all dimensions based on the recent linear profile decomposition results. We then present a new proof of the linear profile decomposition for the Schröindger equation with initial data in the homogeneous Sobolev space; as a consequence, there exists a maximizer for the Sobolev-Strichartz inequality.14 pages; Various corrections, references updatedAnalysis of PDEs35Q55text