The linear profile decomposition for the fourth order Schrödinger equation

Details The linear profile decomposition for the fourth order Schrödinger equation The linear profile decomposition for the fourth order Schrödinger equation

2009-11-04

arxiv.org/abs/0911.0719v1

Mathematics

Analysis of PDEs

27 pages, no figures

Scientific paper

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

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