English

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}
}