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arXiv · 1603.03575

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

Stephan De Bièvre·Arthur Vavasseur·Thierry Goudon
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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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Stephan De Bièvre, Arthur Vavasseur, Thierry Goudon. 2016-03-11. Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov--Poisson system. https://arxiv.org/abs/1603.03575

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