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

Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)5653-5669
Number of pages17
JournalTransactions of the American Mathematical Society
Volume366
Issue number11
StatePublished - 2014

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Klein-Gordon Equation
Nonlinear Klein-Gordon Equation
Scattering
Blow-up
Energy
Ground state
Global Dynamics
Dichotomy
Higher Dimensions
Ground State
Two Dimensions
Nonlinearity

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Transactions of the American Mathematical Society, Vol. 366, No. 11, 2014, p. 5653-5669.

Research output: Contribution to journalArticle

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