Small data scattering for energy-subcritical and critical Nonlinear Klein Gordon equations on product spaces

Abstract

We study small data scattering of solutions to Nonlinear Klein-Gordon equations with suitable pure power nonlinearities, posed on ${\mathbb{R}}^d\times {\mathcal{M}}^k$ with $k\le 2$ and $d\ge 1$ and ${\mathcal{M}}^k$ a compact Riemannian manifold. As a special case we cover the $H^1-$critical NLKG on $\mathbb{R}\times M^2$.