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

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

2011-10-08

arxiv.org/abs/1110.1709v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

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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