Electronic Journal of Differential Equations,
Vol. 2009(2009), No. 03, pp. 1-13.

Title: Maximizers for the Strichartz and the Sobolev-Strichartz
       inequalities for the Schrodinger equation
   
Author: Shuanglin Shao (Inst. for Advanced Study, Princeton, NJ, USA)

Abstract:
 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 02, 2009.
Math Subject Classifications: 35Q55.
Key Words: Maximizers; Profile decomposition; Schrodinger equation;
           Strichartz inequality.