Scattering theory below energy for the cubic fourth-order Schrödinger equation

Changxing Miao; Haigen Wu; Junyong Zhang

doi:10.1002/mana.201400012

Scattering theory below energy for the cubic fourth-order Schrödinger equation

Changxing Miao
, Haigen Wu
, Junyong Zhang^*

^*此作品的通讯作者

数学学院

IAPCM
Beijing Center for Mathematics and Information Interdisciplinary Sciences
Henan Polytechnic University

科研成果: 期刊稿件 › 文章 › 同行评审

29 引用（Scopus）

摘要

We investigate the global existence and scattering for the cubic fourth-order Schrödinger 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.

源语言	英语
页（从-至）	798-823
页数	26
期刊	Mathematische Nachrichten
卷	288
期	7
DOI	https://doi.org/10.1002/mana.201400012
出版状态	已出版 - 1 5月 2015

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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",

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TY - JOUR

T1 - Scattering theory below energy for the cubic fourth-order Schrödinger equation

AU - Miao, Changxing

AU - Wu, Haigen

AU - Zhang, Junyong

PY - 2015/5/1

Y1 - 2015/5/1

N2 - We investigate the global existence and scattering for the cubic fourth-order Schrödinger 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.

AB - We investigate the global existence and scattering for the cubic fourth-order Schrödinger 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.

KW - 35Q40

KW - 35Q55

KW - 47J35

KW - Fourth-order Schrödinger equation

KW - Global well-posedness

KW - Low regularity

KW - Strichartz-type estimate

UR - https://www.scopus.com/pages/publications/84928273609

U2 - 10.1002/mana.201400012

DO - 10.1002/mana.201400012

M3 - Article

AN - SCOPUS:84928273609

SN - 0025-584X

VL - 288

SP - 798

EP - 823

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 7

ER -

Scattering theory below energy for the cubic fourth-order Schrödinger equation

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