  The recently developed theory of Lagrangian flows for transport equations
with low regularity coefficients enables to consider non BV vector fields. We
apply this theory to prove existence and stability of global Lagrangian
solutions to the repulsive Vlasov-Poisson system with only integrable initial
distribution function with finite energy. These solutions have a well-defined
Lagrangian flow. An a priori estimate on the smallness of the superlevels of
the flow in three dimensions is established in order to control the
characteristics.
