In this talk, I will present some recent results on the well-posedness, steady states and long time behavior of the self-consistent Vlasov-Fokker-Planck equation. This equation models a large system of particles which is subject to external confinement, long-range interactions between particles, and thermalization mechanisms. Motivated by applications in particle accelerator physics, I will consider interaction potentials which may be singular and non-symmetric with respect to the relative position of the particles. For asymptotically stable steady states, we obtain quantitative long-time behavior estimates that are not restricted to weakly nonlinear regimes, which improves former results. This talk is based on joint works with Ludovic Cesbron (CY Cergy Paris Université) and Pierre Gervais (Université de Lille).
