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

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.

14 pages; Various corrections, references updated

References in corpus (1)

• Time decay for the bounded mean oscillation of solutions of the Schrödinger and wave equations

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