2016/03/11 by Stephan De Bièvre, De Bièvre, Stephan, Arthur Vavasseur +3
Engineering · Mathematics · #Gas Dynamics and Kinetic Theory #Mathematical Biology Tumor Growth #Particle Dynamics in Fluid Flows #math.AP
paper · pdf · doi:10.48550/arxiv.1603.03575
arxiv created 2016/03/11 · arxiv updated 2016/03/14
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.