Energy concentration of the focusing energy-critical fNLS

Yonggeun Cho; Gyeongha Hwang; Yong Sun Shim

doi:10.1016/j.jmaa.2015.12.060

Energy concentration of the focusing energy-critical fNLS

Yonggeun Cho^*
, Gyeongha Hwang
, Yong Sun Shim

^*Corresponding author for this work

Department of Mathematics

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

2 Scopus citations

Abstract

We consider the fractional nonlinear Schrödinger equation (fNLS) with non-local dispersion |∇|^α and focusing energy-critical Hartree type nonlinearity [-(|x|^-2α*|u|²)u]. We consider the energy-concentration phenomena of radial blowup solutions near the maximal existence time. We use the concentration-compactness approach of [19] for confined case and kinetic energy trapping approach of [21] for unconfined case.

Original language	English
Pages (from-to)	310-329
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	437
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.12.060
State	Published - 2016.05.1

Keywords

Blowup
Concentration compactness
Energy concentration
Energy trapping
Focusing energy-critical fNLS
Global well-posedness

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1016/j.jmaa.2015.12.060

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@article{48f870454219445e86325fe8d901b38f,

title = "Energy concentration of the focusing energy-critical fNLS",

abstract = "We consider the fractional nonlinear Schr{\"o}dinger equation (fNLS) with non-local dispersion |∇|α and focusing energy-critical Hartree type nonlinearity [-(|x|-2α*|u|2)u]. We consider the energy-concentration phenomena of radial blowup solutions near the maximal existence time. We use the concentration-compactness approach of [19] for confined case and kinetic energy trapping approach of [21] for unconfined case.",

keywords = "Blowup, Concentration compactness, Energy concentration, Energy trapping, Focusing energy-critical fNLS, Global well-posedness",

author = "Yonggeun Cho and Gyeongha Hwang and Shim, \{Yong Sun\}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = may,

day = "1",

doi = "10.1016/j.jmaa.2015.12.060",

language = "English",

volume = "437",

pages = "310--329",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

number = "1",

}

TY - JOUR

T1 - Energy concentration of the focusing energy-critical fNLS

AU - Cho, Yonggeun

AU - Hwang, Gyeongha

AU - Shim, Yong Sun

PY - 2016/5/1

Y1 - 2016/5/1

N2 - We consider the fractional nonlinear Schrödinger equation (fNLS) with non-local dispersion |∇|α and focusing energy-critical Hartree type nonlinearity [-(|x|-2α*|u|2)u]. We consider the energy-concentration phenomena of radial blowup solutions near the maximal existence time. We use the concentration-compactness approach of [19] for confined case and kinetic energy trapping approach of [21] for unconfined case.

AB - We consider the fractional nonlinear Schrödinger equation (fNLS) with non-local dispersion |∇|α and focusing energy-critical Hartree type nonlinearity [-(|x|-2α*|u|2)u]. We consider the energy-concentration phenomena of radial blowup solutions near the maximal existence time. We use the concentration-compactness approach of [19] for confined case and kinetic energy trapping approach of [21] for unconfined case.

KW - Blowup

KW - Concentration compactness

KW - Energy concentration

KW - Energy trapping

KW - Focusing energy-critical fNLS

KW - Global well-posedness

UR - https://www.scopus.com/pages/publications/84959108225

U2 - 10.1016/j.jmaa.2015.12.060

DO - 10.1016/j.jmaa.2015.12.060

M3 - Journal article

AN - SCOPUS:84959108225

SN - 0022-247X

VL - 437

SP - 310

EP - 329

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Energy concentration of the focusing energy-critical fNLS

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

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