Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov–Poisson system

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.
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Submitted on : Friday, March 11, 2016 - 12:41:20 AM
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  • HAL Id : hal-01286519, version 1
  • ARXIV : 1603.03575

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Stephan de Bièvre, Arthur Vavasseur, Thierry Goudon. Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov–Poisson system. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2016, 48 (6), pp.3984--4020. ⟨hal-01286519⟩

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