The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality

Shao, Shuanglin

doi:10.2140/apde.2009.2.83

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The linear profile decomposition for the Airy equation and the existence of maximizers for the Airy Strichartz inequality

Shuanglin Shao

Vol. 2 (2009), No. 1, 83–117

DOI: 10.2140/apde.2009.2.83

Abstract

We establish the linear profile decomposition for the Airy equation with complex or real initial data in $L^{2}$ . As an application, we obtain a dichotomy result on the existence of maximizers for the symmetric Airy Strichartz inequality.

Keywords

gKdV, mass-critical, profile decomposition, maximizer

Mathematical Subject Classification 2000

Primary: 35Q53

Milestones

Received: 31 August 2008

Revised: 17 February 2009

Accepted: 17 February 2009

Published: 1 February 2009

Authors

Shuanglin Shao
Department of Mathematics University of California, Los Angeles Los Angeles, CA 90095 United States	School of Mathematics Institute for Advanced Study Princeton, NJ 08540 United States

Vol. 2, No. 1, 2009