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

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

2008-08-31

arxiv.org/abs/0809.0153v4

Mathematics

Analysis of PDEs

14 pages; Various corrections, references updated

Scientific paper

In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr\"odinger 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 Schr\"oindger equation with initial data in the homogeneous Sobolev space; as a consequence, there exists a maximizer for the Sobolev-Strichartz inequality.

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