Electron. J. Diff. Eqns., Vol. 2009(2009), No. 03, pp. 1-13.

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

Shuanglin Shao

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.

Submitted October 13, 2008. Published January 2, 2009.
Math Subject Classifications: 35Q55.
Key Words: Maximizers; Profile decomposition; Schrodinger equation; Strichartz inequality.

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Shuanglin Shao
Department of Mathematics
University of California, CA 90095, USA.
Institute for Advanced Study, Princeton, NJ 08540, USA
email: slshao@math.ias.edu

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