Scattering theory below energy for a class of Hartree type equations

Myeongju Chae; Sunggeum Hong; Joonil Kim; Chan Woo Yang

doi:10.1080/03605300701629427

Scattering theory below energy for a class of Hartree type equations

Myeongju Chae^*
, Sunggeum Hong
, Joonil Kim
, Chan Woo Yang

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

We prove the global existence and scattering for the Hartree-type equation in H^s(3) the low regularity space s<1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the Lp estimate in Coifman and Meyer (1978).

Original language	English
Pages (from-to)	321-348
Number of pages	28
Journal	Communications in Partial Differential Equations
Volume	33
Issue number	3
DOIs	https://doi.org/10.1080/03605300701629427
Publication status	Published - 2008 Mar

Bibliographical note

Funding Information:
The first author would like to thank Korea Institute for Advanced Study (KIAS) for support. The first author was supported by the Korea Research Foundation (KRF-2007-C00020). The second and the fourth authors were supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00457).

Keywords

Nonlinear Hartree-type Schrödinger equation
Well-posedness

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1080/03605300701629427

Cite this

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title = "Scattering theory below energy for a class of Hartree type equations",

abstract = "We prove the global existence and scattering for the Hartree-type equation in Hs(3) the low regularity space s<1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the Lp estimate in Coifman and Meyer (1978).",

keywords = "Nonlinear Hartree-type Schr{\"o}dinger equation, Well-posedness",

author = "Myeongju Chae and Sunggeum Hong and Joonil Kim and Yang, \{Chan Woo\}",

note = "Funding Information: The first author would like to thank Korea Institute for Advanced Study (KIAS) for support. The first author was supported by the Korea Research Foundation (KRF-2007-C00020). The second and the fourth authors were supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00457).",

year = "2008",

month = mar,

doi = "10.1080/03605300701629427",

language = "English",

volume = "33",

pages = "321--348",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

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TY - JOUR

T1 - Scattering theory below energy for a class of Hartree type equations

AU - Chae, Myeongju

AU - Hong, Sunggeum

AU - Kim, Joonil

AU - Yang, Chan Woo

N1 - Funding Information: The first author would like to thank Korea Institute for Advanced Study (KIAS) for support. The first author was supported by the Korea Research Foundation (KRF-2007-C00020). The second and the fourth authors were supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00457).

PY - 2008/3

Y1 - 2008/3

N2 - We prove the global existence and scattering for the Hartree-type equation in Hs(3) the low regularity space s<1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the Lp estimate in Coifman and Meyer (1978).

AB - We prove the global existence and scattering for the Hartree-type equation in Hs(3) the low regularity space s<1. We follow the ideas in Colliander et al. (2004) to the Hartree-type nonlinearity, and also develop the theory of the classical multilinear operator modifying the Lp estimate in Coifman and Meyer (1978).

KW - Nonlinear Hartree-type Schrödinger equation

KW - Well-posedness

UR - https://www.scopus.com/pages/publications/40249105842

U2 - 10.1080/03605300701629427

DO - 10.1080/03605300701629427

M3 - Article

AN - SCOPUS:40249105842

SN - 0360-5302

VL - 33

SP - 321

EP - 348

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 3

ER -

Scattering theory below energy for a class of Hartree type equations

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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