### 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 |

State | Published - 2014 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*366*(11), 5653-5669.

**Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation.** / Ibrahim, Slim; Masmoudi, Nader; Nakanishi, Kenji.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 366, no. 11, pp. 5653-5669.

}

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

M3 - Article

VL - 366

SP - 5653

EP - 5669

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 11

ER -