Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation

2008/08/31 by Shuanglin Shao, Shao, Shuanglin
Mathematics · #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0809.0153

openalex publication_date 2008/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 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.

Related

• Maximizers for the Strichartz inequality
• Existence of maximizers for Sobolev-Strichartz inequalities
• Critical points of Strichartz functional
• Strichartz Estimates for the Schrödinger Equation
• Linear profile decompositions for a family of fourth order Schrödinger equations