Shao, Shuanglin2015-03-242015-03-242009-09-04Shao, Shuanglin. "Maximizers for the Strichartz and the Sobolev-Strichartz inequalities for the Schrödinger equation." (2009) Electronic Journal of Differential Equations. Vol 3. pg. 1-13. http://ejde.math.txstate.edu/https://hdl.handle.net/1808/17188This is the published version, also available here: http://ejde.math.txstate.edu/.In this paper, we first show that there exists a maximizer for the non-endpoint Strichartz inequalities for the Schr¨odinger 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 Schr¨oindger equation with initial data in the homogeneous Sobolev space; as a consequence, there exists a maximizer for the Sobolev-Strichartz inequality.ArticleopenAccess