Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation

Slim Ibrahim; Nader Masmoudi; Kenji Nakanishi

doi:10.1090/S0002-9947-2014-05852-2

Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation

Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi

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

Abstract

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy extends to the threshold energy in the case of mass-shift for the critical nonlinear Klein-Gordon equation.

Original language	English (US)
Pages (from-to)	5653-5669
Number of pages	17
Journal	Transactions of the American Mathematical Society
Volume	366
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9947-2014-05852-2
State	Published - 2014

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9947-2014-05852-2

Cite this

@article{d36d7890901e49b98c16c471b42c11bf,

title = "Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation",

abstract = "We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy extends to the threshold energy in the case of mass-shift for the critical nonlinear Klein-Gordon equation.",

author = "Slim Ibrahim and Nader Masmoudi and Kenji Nakanishi",

note = "Publisher Copyright: {\textcopyright} 2014 American Mathematical Society.",

year = "2014",

doi = "10.1090/S0002-9947-2014-05852-2",

language = "English (US)",

volume = "366",

pages = "5653--5669",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "11",

}

TY - JOUR

T1 - Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation

AU - Ibrahim, Slim

AU - Masmoudi, Nader

AU - Nakanishi, Kenji

PY - 2014

Y1 - 2014

N2 - We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy extends to the threshold energy in the case of mass-shift for the critical nonlinear Klein-Gordon equation.

AB - We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy extends to the threshold energy in the case of mass-shift for the critical nonlinear Klein-Gordon equation.

UR - http://www.scopus.com/inward/record.url?scp=84903796007&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903796007&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2014-05852-2

DO - 10.1090/S0002-9947-2014-05852-2

M3 - Article

AN - SCOPUS:84903796007

SN - 0002-9947

VL - 366

SP - 5653

EP - 5669

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 11

ER -

Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this