A Critical Density Estimate for the Vlasov--Poisson System: Energy Conservation and Moment Propagation

Zhaopeng Wang

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arXiv · 2607.26840

A Critical Density Estimate for the Vlasov--Poisson System: Energy Conservation and Moment Propagation

Zhaopeng Wang

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Abstract

This paper establishes a critical space--time density estimate for the three-dimensional Vlasov--Poisson system in the whole space and on the torus. This estimate has two consequences. First, every nonnegative weak solution with finite initial kinetic energy in the bounded finite-energy weak-solution class conserves the total energy. This gives a positive answer, within this class, to the energy-conservation question raised by Lions and Perthame. Second, in the periodic repulsive case, it yields propagation of every velocity moment of order $k>2$, thereby closing the previously unresolved interval $2<k\leq3$.

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Zhaopeng Wang. 2026-07-29. A Critical Density Estimate for the Vlasov--Poisson System: Energy Conservation and Moment Propagation. https://arxiv.org/abs/2607.26840

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