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
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