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

Ibrahim, Slim; Masmoudi, Nader; Nakanishi, Kenji

doi:10.1090/S0002-9947-2014-05852-2

Threshold solutions in the case of mass-shift for the critical Klein-Gordon equation
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by Slim Ibrahim, Nader Masmoudi and Kenji Nakanishi PDF

Trans. Amer. Math. Soc. 366 (2014), 5653-5669 Request permission

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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