Strichartz estimates for Klein-Gordon equations with moving potentials

TL;DR

This paper establishes Strichartz estimates, local energy decay, and scattering theory for Klein-Gordon equations with moving potentials, aiding the analysis of soliton interactions and stability in nonlinear models.

Contribution

It introduces new Strichartz estimates and scattering results for Klein-Gordon equations with moving potentials, advancing the understanding of soliton dynamics.

Findings

Established Strichartz estimates for moving potential models

Proved local energy decay and scattering theory results

Provided tools for analyzing soliton interactions and stability

Abstract

We study linear Klein-Gordon equations with moving potentials motivated by the stability analysis of traveling waves and multi-solitons. In this paper, Strichartz estimates, local energy decay and the scattering theory for these models are established. The results and estimates obtained in this paper will be used to study the interaction of solitons and the stability of multisolitons of nonlinear Klein-Gordon equations.