Modified scattering dynamics in the Vlasov-Poisson equation near an attractive point mass

Abstract: We study the long-time behavior of radially symmetric solutions to the Vlasov-Poisson equation consisting of an attractive point mass and a small, suitably localized and absolutely continuous distribution of particles: if the latter is initially localized on hyperbolic trajectories for the associated Kepler problem, we obtain global in time, unique Lagrangian solutions that asymptotically undergo a modified scattering dynamics (in the sense of distributions). A key feature of this result is its low regularity regime, which does not make use of derivative control, but can be upgraded to strong solutions and strong convergence by propagation of regularity.