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

In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schrodinger equation in all dimensions based on the recent linear profile decomposition result. We then present a new proof of the linear profile decomposition for the Schroindger 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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