Finite energy scattering for the Lorentz-Maxwell equation
Analysis of PDEs
2009-11-13 v1
Abstract
In the case where the charge of the particle is small compared to its mass, we describe the asymptotics of the Lorentz-Maxwell equation for any finite-energy data. As time goes to infinity, we prove that the speed of the particle converges to a certain limit, whereas the electromagnetic field can be decomposed into a soliton plus a free solution of the Maxwell equation. It is the first instance of a scattering result for general finite energy data in a field-particle equation.
Cite
@article{arxiv.0806.4153,
title = {Finite energy scattering for the Lorentz-Maxwell equation},
author = {Pierre Germain},
journal= {arXiv preprint arXiv:0806.4153},
year = {2009}
}