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^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	798-823
Number of pages	26
Journal	Mathematische Nachrichten
Volume	288
Issue number	7
DOIs	https://doi.org/10.1002/mana.201400012
Publication status	Published - 1 May 2015

Keywords

35Q40
35Q55
47J35
Fourth-order Schrödinger equation
Global well-posedness
Low regularity
Strichartz-type estimate

Access to Document

10.1002/mana.201400012

Cite this

@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",

}

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 - http://www.scopus.com/inward/record.url?scp=84928273609&partnerID=8YFLogxK

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this