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.
|Original language||English (US)|
|Number of pages||17|
|Journal||Transactions of the American Mathematical Society|
|State||Published - 2014|
ASJC Scopus subject areas
- Applied Mathematics