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

TL;DR

This paper investigates the scattering behavior of solutions to energy-subcritical and critical nonlinear Klein-Gordon equations on product spaces, extending understanding of wave dynamics in mixed Euclidean and compact geometries.

Contribution

It provides new results on small data scattering for NLKG equations on product spaces with low-dimensional compact manifolds, including the critical case on -dimensional manifolds.

Findings

Established small data scattering results for energy-subcritical NLKG.

Extended analysis to the -critical NLKG on -dimensional manifolds.

Covered cases with   and compact manifolds .

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 $k\leq2$ and $d\geq1$ and $\mathcal{M}^k$ a compact Riemannian manifold. As a special case we cover the $H^1-$critical NLKG on $\mathbb{R} \times M^2$.