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

Abstract

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

34 pages.A sign error is corrected throught the paper; the statement of Theorem 1.9 is slightly modified since version 3; add a new reference in remark 1.7; some improvement in exposition. To appear Analysis and PDE

References in corpus (4)

• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• A sharp bilinear restriction estimate for paraboloids
• Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation
• Heat-flow monotonicity of Strichartz norms

Cited by in corpus (1)

• The mass-critical fourth-order Schrodinger equation in high dimensions