Remarks on the semirelativistic Hartree equations

Yonggeun Cho; Tohru Ozawa; Hironobu Sasaki; Yongsun Shim

doi:10.3934/dcds.2009.23.1277

Remarks on the semirelativistic Hartree equations

Yonggeun Cho^*, Tohru Ozawa, Hironobu Sasaki, Yongsun Shim

^*Corresponding author for this work

School of Advanced Science and Engineering

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

19 Citations (Scopus)

Abstract

We study the global well-posedness (GWP) and small data scattering of radial solutions of the semirelativistic Hartree type equations with nonlocal nonlinearity F(u) = λ(| · |^-γ * |u| ²)u, λ ∈ ℝ \ {0}, 0 < γ < n, n ≥ 3. We establish a weighted L² Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions.

Original language	English
Pages (from-to)	1277-1294
Number of pages	18
Journal	Discrete and Continuous Dynamical Systems
Volume	23
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2009.23.1277
Publication status	Published - 2009 Apr

Keywords

Global well-posedness
Radial solutions
Scattering
Semirelativistic hartree type equations

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcds.2009.23.1277

Cite this

@article{c390c2573e0340c99d697c067a053e29,

title = "Remarks on the semirelativistic Hartree equations",

abstract = "We study the global well-posedness (GWP) and small data scattering of radial solutions of the semirelativistic Hartree type equations with nonlocal nonlinearity F(u) = λ(| · |-γ * |u| 2)u, λ ∈ ℝ \ {0}, 0 < γ < n, n ≥ 3. We establish a weighted L2 Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions.",

keywords = "Global well-posedness, Radial solutions, Scattering, Semirelativistic hartree type equations",

author = "Yonggeun Cho and Tohru Ozawa and Hironobu Sasaki and Yongsun Shim",

year = "2009",

month = apr,

doi = "10.3934/dcds.2009.23.1277",

language = "English",

volume = "23",

pages = "1277--1294",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "4",

}

TY - JOUR

T1 - Remarks on the semirelativistic Hartree equations

AU - Cho, Yonggeun

AU - Ozawa, Tohru

AU - Sasaki, Hironobu

AU - Shim, Yongsun

PY - 2009/4

Y1 - 2009/4

N2 - We study the global well-posedness (GWP) and small data scattering of radial solutions of the semirelativistic Hartree type equations with nonlocal nonlinearity F(u) = λ(| · |-γ * |u| 2)u, λ ∈ ℝ \ {0}, 0 < γ < n, n ≥ 3. We establish a weighted L2 Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions.

AB - We study the global well-posedness (GWP) and small data scattering of radial solutions of the semirelativistic Hartree type equations with nonlocal nonlinearity F(u) = λ(| · |-γ * |u| 2)u, λ ∈ ℝ \ {0}, 0 < γ < n, n ≥ 3. We establish a weighted L2 Strichartz estimate applicable to non-radial functions and some fractional integral estimates for radial functions.

KW - Global well-posedness

KW - Radial solutions

KW - Scattering

KW - Semirelativistic hartree type equations

UR - http://www.scopus.com/inward/record.url?scp=62649143305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62649143305&partnerID=8YFLogxK

U2 - 10.3934/dcds.2009.23.1277

DO - 10.3934/dcds.2009.23.1277

M3 - Article

AN - SCOPUS:62649143305

SN - 1078-0947

VL - 23

SP - 1277

EP - 1294

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

IS - 4

ER -

Remarks on the semirelativistic Hartree equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this