On small data scattering of Hartree equations with short-range interaction

Yonggeun Cho; Gyeongha Hwang; Tohru Ozawa

doi:10.3934/cpaa.2016016

On small data scattering of Hartree equations with short-range interaction

Yonggeun Cho, Gyeongha Hwang^*, Tohru Ozawa

^*この研究の対応する著者

先進理工学部

研究成果: Article › 査読

8 被引用数 (Scopus)

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In this note we study Hartree type equations with |∇| ^α (1 < α ≤ 2) and potential whose Fourier transform behaves like |ξ| ^{- (d- γ1)} at the origin and |ξ| ^{- (d- γ2)} at infinity. We show non-existence of scattering when 0 < 1 γ ≤ 1 and small data scattering in H^s for s > 2-α/2 when 2 < γ1 ≤ d and 0 < γ2 ≤ 2. For this we use U^p - V^p space argument and Strichartz estimate.

本文言語	English
ページ（範囲）	1809-1823
ページ数	15
ジャーナル	Communications on Pure and Applied Analysis
巻	15
号	5
DOI	https://doi.org/10.3934/cpaa.2016016
出版ステータス	Published - 2016 9月

ASJC Scopus subject areas

分析
応用数学

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abstract = "In this note we study Hartree type equations with |∇| α (1 < α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 < 1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 < γ1 ≤ d and 0 < γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.",

keywords = "Hartree equations, Short range potential, Small data scattering, Up and V p spaces",

author = "Yonggeun Cho and Gyeongha Hwang and Tohru Ozawa",

year = "2016",

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doi = "10.3934/cpaa.2016016",

language = "English",

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T1 - On small data scattering of Hartree equations with short-range interaction

AU - Cho, Yonggeun

AU - Hwang, Gyeongha

AU - Ozawa, Tohru

PY - 2016/9

Y1 - 2016/9

N2 - In this note we study Hartree type equations with |∇| α (1 < α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 < 1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 < γ1 ≤ d and 0 < γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.

AB - In this note we study Hartree type equations with |∇| α (1 < α ≤ 2) and potential whose Fourier transform behaves like |ξ| - (d- γ1) at the origin and |ξ| - (d- γ2) at infinity. We show non-existence of scattering when 0 < 1 γ ≤ 1 and small data scattering in Hs for s > 2-α/2 when 2 < γ1 ≤ d and 0 < γ2 ≤ 2. For this we use Up - Vp space argument and Strichartz estimate.

KW - Hartree equations

KW - Short range potential

KW - Small data scattering

KW - Up and V p spaces

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SN - 1534-0392

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SP - 1809

EP - 1823

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 5

ER -

On small data scattering of Hartree equations with short-range interaction

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