2026/08/05 by Wenrui Huang, Mengyi Xie
Mathematics · #math.AP
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We study the three-dimensional Vlasov--Hartree system with Coulomb interaction, a classical--quantum model for Bose--Fermi mixtures. For sufficiently small, regular, and localized initial data, we prove global well-posedness and determine the precise long-time dynamics. The coupling remains visible at leading order: the Vlasov distribution scatters along logarithmically corrected free characteristics determined by the asymptotic bosonic profile, while the Hartree wave acquires a logarithmic phase correction generated by the asymptotic fermionic density. Our proof combines techniques from kinetic theory with vector-field methods for dispersive equations and also extends to shorter-range inverse-power interactions.