Global existence for the defocusing masscritical nonlinear fourthorder Schrödinger equation below the energy space
Abstract
In this paper, we consider the defocusing masscritical nonlinear fourthorder Schrödinger equation. Using the $I$method combined with the interaction Morawetz estimate, we prove that the problem is globally wellposed in $H^\gamma(\mathbb{R}^d), 5\leq d\leq 7$ with $\gamma(d)<\gamma<2$, where $\gamma(5)=\frac{8}{5}, \gamma(6)=\frac{5}{3}$ and $\gamma(7)=\frac{13}{7}$.
 Publication:

arXiv eprints
 Pub Date:
 June 2017
 DOI:
 10.48550/arXiv.1706.06517
 arXiv:
 arXiv:1706.06517
 Bibcode:
 2017arXiv170606517D
 Keywords:

 Mathematics  Analysis of PDEs
 EPrint:
 20 pages