On the energy-critical fractional schrödinger equation in the radial case

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On the energy-critical fractional schrödinger equation in the radial case. / Guo, Zihua; Sire, Yannick; Wang, Yuzhao; Zhao, Lifeng.

In: Dynamics of Partial Differential Equations, Vol. 15, No. 4, 05.12.2018, p. 265-282.

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Guo, Zihua ; Sire, Yannick ; Wang, Yuzhao ; Zhao, Lifeng. / On the energy-critical fractional schrödinger equation in the radial case. In: Dynamics of Partial Differential Equations. 2018 ; Vol. 15, No. 4. pp. 265-282.

Bibtex

@article{37e20bf88e1044a9aba5ff0a19c027d4,
title = "On the energy-critical fractional schr{\"o}dinger equation in the radial case",
abstract = "We consider the Cauchy problem for the energy-critical nonlinear Schr{\"o}dinger equation with fractional Laplacian (fNLS) in the radial case. We obtain global well-posedness and scattering in the energy space in the defo-cusing case, and in the focusing case with energy below the ground state. The main feature of the present work is the nonlocality of the operator. This does not allow us to use standard computations for the rigidity part of the theorem. Instead we develop a commutator argument which has its own interest for problems with nonlocal operators.",
keywords = "Nonlinear Schr{\"o}dinger equation, Nonlinear wave equation",
author = "Zihua Guo and Yannick Sire and Yuzhao Wang and Lifeng Zhao",
year = "2018",
month = dec,
day = "5",
doi = "10.4310/DPDE.2018.V15.N4.A2",
language = "English",
volume = "15",
pages = "265--282",
journal = "Dynamics of Partial Differential Equations",
issn = "1548-159X",
publisher = "International Press of Boston, Inc.",
number = "4",

}

RIS

TY - JOUR

T1 - On the energy-critical fractional schrödinger equation in the radial case

AU - Guo, Zihua

AU - Sire, Yannick

AU - Wang, Yuzhao

AU - Zhao, Lifeng

PY - 2018/12/5

Y1 - 2018/12/5

N2 - We consider the Cauchy problem for the energy-critical nonlinear Schrödinger equation with fractional Laplacian (fNLS) in the radial case. We obtain global well-posedness and scattering in the energy space in the defo-cusing case, and in the focusing case with energy below the ground state. The main feature of the present work is the nonlocality of the operator. This does not allow us to use standard computations for the rigidity part of the theorem. Instead we develop a commutator argument which has its own interest for problems with nonlocal operators.

AB - We consider the Cauchy problem for the energy-critical nonlinear Schrödinger equation with fractional Laplacian (fNLS) in the radial case. We obtain global well-posedness and scattering in the energy space in the defo-cusing case, and in the focusing case with energy below the ground state. The main feature of the present work is the nonlocality of the operator. This does not allow us to use standard computations for the rigidity part of the theorem. Instead we develop a commutator argument which has its own interest for problems with nonlocal operators.

KW - Nonlinear Schrödinger equation

KW - Nonlinear wave equation

UR - http://www.scopus.com/inward/record.url?scp=85060187706&partnerID=8YFLogxK

U2 - 10.4310/DPDE.2018.V15.N4.A2

DO - 10.4310/DPDE.2018.V15.N4.A2

M3 - Article

AN - SCOPUS:85060187706

VL - 15

SP - 265

EP - 282

JO - Dynamics of Partial Differential Equations

JF - Dynamics of Partial Differential Equations

SN - 1548-159X

IS - 4

ER -