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

2011/10/08 by Slim Ibrahim, Nader Masmoudi, Ibrahim, Slim +3
Engineering · Mathematics · Physics and Astronomy · #35B40 #35B44 #35L70 #47J30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations #math.AP #msc:35B40 #msc:35B44 #msc:35L70 #msc:47J30

paper · pdf · doi:10.48550/arxiv.1110.1709

16 pages

arxiv created 2011/10/08 · openalex publication_date 2011/10/08 · arxiv updated 2011/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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