Year: 2008
Type: preprint
Abstract: We investigate the cubic defocusing fourth order Schrödinger equation $iu_t + Δ^2u + |u|^2u=0$ in arbitrary space dimension $\mathbb{R}^n$ for arbitrary $H^2$ initial data. We prove that the equation is globally well-posed when $n \le 8$ and ill-posed when $n \ge 9$, with the additional important information that scattering holds true when $5 \le n \le 8$.
Source: arXiv (Cornell University)
Author: Pausader, Benoit
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950144033