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<p>We investigate the classical limit of global classical solutions to the relativistic Vlasov-Darwin system with generalized variables. Under the assumption of sufficiently small and compactly supported initial data, we prove that the relativistic dynamics converge to those of the Vlasov-Poisson system as the speed of light tends to infinity. In particular, we establish pointwise convergence of the distribution function with an explicit rate of order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(O(C^{-1})\)</EquationSource> </InlineEquation> together with quantitative estimates for the associated scalar and vector potentials. Moreover, sharp decay estimates describing the long-time asymptotic behavior of the solutions are derived. The analysis is based on characteristic methods and refined comparison arguments between relativistic and non-relativistic flows, and provides the first rigorous justification of the classical limit for the generalized Vlasov-Darwin framework.</p>

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Classical Limit and Asymptotic Behaviour of Relativistic Vlasov-Darwin System with Generalized Variables

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月13日

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  • Yaxian Ma,
  • Dong Qiao

摘要

We investigate the classical limit of global classical solutions to the relativistic Vlasov-Darwin system with generalized variables. Under the assumption of sufficiently small and compactly supported initial data, we prove that the relativistic dynamics converge to those of the Vlasov-Poisson system as the speed of light tends to infinity. In particular, we establish pointwise convergence of the distribution function with an explicit rate of order \(O(C^{-1})\) together with quantitative estimates for the associated scalar and vector potentials. Moreover, sharp decay estimates describing the long-time asymptotic behavior of the solutions are derived. The analysis is based on characteristic methods and refined comparison arguments between relativistic and non-relativistic flows, and provides the first rigorous justification of the classical limit for the generalized Vlasov-Darwin framework.