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Moment Propagation for the Vlasov--Poisson System with Gyroscopic Forces, Velocity Diffusion, and Specular Reflection
Abstract
This paper studies the three-dimensional Vlasov--Poisson system with gyroscopic forces and velocity diffusion. For the Cauchy problem in ℝ3 and the specular--Dirichlet problem in bounded domains, we prove the propagation of velocity moments of order k>2 for weak solutions with bounded L1∩ L∞ norms and kinetic energy. The proof applies Serre's compensated integrability to weighted mass--momentum tensors to derive density estimates. A finite iteration alternating moment propagation with improved density integrability then closes the estimates. These estimates provide a simplified approach to moment propagation and yield global continuation of classical solutions.
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BibTeX
@misc{wu2026moment,
title = {{Moment Propagation for the Vlasov--Poisson System with Gyroscopic Forces, Velocity Diffusion, and Specular Reflection}},
author = {Jingpeng Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21745},
eprint = {2610.21745},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21745},
}
RIS
TY - UNPB
TI - Moment Propagation for the Vlasov--Poisson System with Gyroscopic Forces, Velocity Diffusion, and Specular Reflection
AU - Jingpeng Wu
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21745
UR - https://arxiv.org/abs/2610.21745
AB - This paper studies the three-dimensional Vlasov--Poisson system with gyroscopic forces and velocity diffusion. For the Cauchy problem in ℝ^3 and the specular--Dirichlet problem in bounded domains, we prove the propagation of velocity moments of order k>2 for weak solutions with bounded L^1∩ L^∞ norms and kinetic energy. The proof applies Serre's compensated integrability to weighted mass--momentum tensors to derive density estimates. A finite iteration alternating moment propagation with improved density integrability then closes the estimates. These estimates provide a simplified approach to moment propagation and yield global continuation of classical solutions.
ER -