Global solutions of multispeed semilinear Klein-Gordon systems in space dimension two

Abstract

We consider general semilinear, multispeed Klein-Gordon systems in space dimension two with some non-degeneracy conditions. We prove that with small initial data such solutions are always global and scatter to a linear solution. This result partly extends the previous result obtained by Deng [3], who completely proved the 3D quasilinear case. To prove our result, we mainly work on Fourier side and explore the contribution from the vicinity of space-time resonance.