Particles interacting with a vibrating medium: existence of solutions   and convergence to the Vlasov--Poisson system
  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. 
Stephan De Bi\`evre (MEPHYSTO), Arthur Vavasseur (COFFEE, JAD),   Thierry Goudon (COFFEE, JAD)
math.AP