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

By Slim Ibrahim, Nader Masmoudi and Kenji Nakanishi

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.Comment: 16 page

Topics: Mathematics - Analysis of PDEs, 35L70, 35B40, 35B44, 47J30
Year: 2011
OAI identifier: oai:arXiv.org:1110.1709

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