Short-range scattering of Hartree type fractional NLS II

Yonggeun Cho; Tohru Ozawa

doi:10.1016/j.na.2017.03.005

Short-range scattering of Hartree type fractional NLS II

Yonggeun Cho, Tohru Ozawa

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

4 Citations (Scopus)

Abstract

We prove the small data scattering for Hartree type fractional Schrödinger equation with inverse square potential. This is the border line problem between Strichartz range and weighted space range in view of the method of approach. To show this we carry out a subtle trilinear estimate via fractional Leibniz rule and Balakrishnan's formula. This paper is a sequel of the previous result (Cho, 2017).

Original language	English
Pages (from-to)	62-75
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	157
DOIs	https://doi.org/10.1016/j.na.2017.03.005
Publication status	Published - 2017 Jul 1

Keywords

Hartree type fractional NLS
Inverse square potential
Short-range interaction
Small data scattering

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.na.2017.03.005

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title = "Short-range scattering of Hartree type fractional NLS II",

abstract = "We prove the small data scattering for Hartree type fractional Schr{\"o}dinger equation with inverse square potential. This is the border line problem between Strichartz range and weighted space range in view of the method of approach. To show this we carry out a subtle trilinear estimate via fractional Leibniz rule and Balakrishnan's formula. This paper is a sequel of the previous result (Cho, 2017).",

keywords = "Hartree type fractional NLS, Inverse square potential, Short-range interaction, Small data scattering",

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AU - Ozawa, Tohru

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N2 - We prove the small data scattering for Hartree type fractional Schrödinger equation with inverse square potential. This is the border line problem between Strichartz range and weighted space range in view of the method of approach. To show this we carry out a subtle trilinear estimate via fractional Leibniz rule and Balakrishnan's formula. This paper is a sequel of the previous result (Cho, 2017).

AB - We prove the small data scattering for Hartree type fractional Schrödinger equation with inverse square potential. This is the border line problem between Strichartz range and weighted space range in view of the method of approach. To show this we carry out a subtle trilinear estimate via fractional Leibniz rule and Balakrishnan's formula. This paper is a sequel of the previous result (Cho, 2017).

KW - Hartree type fractional NLS

KW - Inverse square potential

KW - Short-range interaction

KW - Small data scattering

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