Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov--Poisson system
Analysis of PDEs
2016-03-14 v1
Abstract
We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak solutions for a wide class of initial data and external forces. We also identify a relevant regime which allows us to derive, quite surprisingly, the attractive Vlasov--Poisson system from the coupled Vlasov-Wave equations.
Keywords
Cite
@article{arxiv.1603.03575,
title = {Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov--Poisson system},
author = {Stephan De Bièvre and Arthur Vavasseur and Thierry Goudon},
journal= {arXiv preprint arXiv:1603.03575},
year = {2016}
}