The linear profile decomposition for the fourth order Schrödinger equation

Abstract

In this paper, we establish the linear profile decomposition for the one dimensional fourth order Schrödinger equation $$i{u}_t-\mu \Delta u+{\Delta }^{2}u=0,t\in \mathbb{R},x\in \mathbb{R},u(0,x)=f(x)\in L^2,$$ where $\mu \ge 0$. As an application, we establish a dichotomy result on the existence of extremals to the symmetric Schrödinger Strichartz inequality.

27 pages, no figures

References in corpus (2)

• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Maximizers for the Strichartz inequalities and the Sobolev-Strichartz inequalities for the Schrödinger equation