The Vlasov-Poisson system with radiation damping

TL;DR

This paper develops and analyzes a simplified kinetic model of radiation damping inspired by post-Newtonian hydrodynamics, demonstrating global well-posedness and decay of fields, avoiding runaway solutions.

Contribution

It introduces a kinetic theory-based model of radiation damping with proven global existence and decay properties, free from runaway solutions.

Findings

Global well-posedness of the model

Fields decay to zero at late times

Model is free from runaway solutions

Abstract

We set up and analyze a model of radiation damping within the framework of continuum mechanics, inspired by a model of post-Newtonian hydrodynamics due to Blanchet, Damour and Schaefer. In order to simplify the problem as much as possible we replace the gravitational field by the electromagnetic field and the fluid by kinetic theory. We prove that the resulting system has a well-posed Cauchy problem globally in time for general initial data and in all solutions the fields decay to zero at late times. In particular, this means that the model is free from the runaway solutions which frequently occur in descriptions of radiation reaction.