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arXiv · 1110.1709

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

Slim Ibrahim·Nader Masmoudi·Kenji Nakanishi
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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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Slim Ibrahim, Nader Masmoudi, Kenji Nakanishi. 2011-10-08. Threshold solutions in the case of mass-shift for the critical Kline-Gordon equation. https://arxiv.org/abs/1110.1709

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