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

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

9 Scopus citations

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 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.

Original language	English
Pages (from-to)	1809-1823
Number of pages	15
Journal	Communications on Pure and Applied Analysis
Volume	15
Issue number	5
DOIs	https://doi.org/10.3934/cpaa.2016016
State	Published - 2016.09

Keywords

Hartree equations
Short range potential
Small data scattering
Up and V p spaces

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10.3934/cpaa.2016016

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title = "On small data scattering of Hartree equations with short-range interaction",

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",

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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

UR - https://www.scopus.com/pages/publications/84977638630

U2 - 10.3934/cpaa.2016016

DO - 10.3934/cpaa.2016016

M3 - Journal article

AN - SCOPUS:84977638630

SN - 1534-0392

VL - 15

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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Keywords

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