A Coulomb-Corrected Labeled Energy and Growth Estimates for the Vlasov-Poisson System

This paper introduces a Coulomb-corrected labeled energy for smooth compactly supported solutions of the three-dimensional repulsive Vlasov--Poisson system.

The resulting identity replaces the direct electric-field term along a characteristic by a weighted singular integral, which can be estimated more effectively.

Thus this structure yields improved bounds on the velocity support and the decay of the electric field.