@article{6fb6a309791d43e6ae903f032e3284c3,
title = "Scattering theory below energy for the cubic fourth-order Schr{\"o}dinger equation",
abstract = "We investigate the global existence and scattering for the cubic fourth-order Schr{\"o}dinger equation iut+Δ2u+|u|2u=0 in a low regularity space Hs(Rn) with s<2. We provide an alternative approach to obtain a new interaction Morawetz estimate which extends the range of the dimension of the interaction Morawetz estimate in Pausader . We utilize the interaction Morawetz estimates and the I-method to prove the global well-posed and scattering result.",
keywords = "35Q40, 35Q55, 47J35, Fourth-order Schr{\"o}dinger equation, Global well-posedness, Low regularity, Strichartz-type estimate",
author = "Changxing Miao and Haigen Wu and Junyong Zhang",
note = "Publisher Copyright: {\textcopyright} 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.",
year = "2015",
month = may,
day = "1",
doi = "10.1002/mana.201400012",
language = "English",
volume = "288",
pages = "798--823",
journal = "Mathematische Nachrichten",
issn = "0025-584X",
publisher = "Wiley-VCH Verlag",
number = "7",
}