Convergence of a multi-fluid scheme for the Vlasov--Poisson system

In this paper, we introduce a novel multi-fluid approximation scheme for the one-dimensional Vlasov-Poisson system, that is relevant for arbitrarily long time intervals. For low regularity solutions, we establish an error estimate in the Wasserstein-1 distance, obtaining a convergence rate of order $O(h^{\frac{2}{3}})$, where h denotes the velocity grid size. This establishes the consistency, as the grid size tends to zero, between the pressureless Euler-Poisson and the Vlasov-Poisson systems. Numerical illustrations are given to illustrate the efficiency of our approach.

Source: arXiv:2609.18810v1 - http://arxiv.org/abs/2609.18810v1 PDF: https://arxiv.org/pdf/2609.18810v1 Original Link: http://arxiv.org/abs/2609.18810v1