标题： 球对称Vlasov-Poisson系统的稳态作为质量保持算法的不动点 显示英文标题

标题： Steady states of the spherically symmetric Vlasov-Poisson system as fixed points of a mass-preserving algorithm

摘要： 我们给出了一种新的证明，用于证明Vlasov-Poisson系统球对称稳态解的存在性，采用了一种已被成功用于数值近似轴对称解的策略，既适用于Vlasov-Poisson系统，也适用于Einstein-Vlasov系统。 对这一数值方案进行数学分析有几个重要原因。 将目前的结果推广到平坦轴对称解的情况，将证明在\cite{AR3}中数值获得的稳态解确实存在。 此外，在相对论情况下，通过该方案能否获得稳态似乎与其动态稳定性有关。 这促使人们希望更深入地理解这一策略。 显示英文摘要

摘要： We give a new proof for the existence of spherically symmetric steady states to the Vlasov-Poisson system, following a strategy that has been used successfully to approximate axially symmetric solutions numerically, both to the Vlasov-Poisson system and to the Einstein-Vlasov system. There are several reasons why a mathematical analysis of this numerical scheme is important. A generalization of the present result to the case of flat axially symmetric solutions would prove that the steady states obtained numerically in \cite{AR3} do exist. Moreover, in the relativistic case the question whether a steady state can be obtained by this scheme seems to be related to its dynamical stability. This motivates the desire for a deeper understanding of this strategy.