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<p>We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty [<CitationRef CitationID="CR14">14</CitationRef>] and Bresch-Jabin-Wang [<CitationRef CitationID="CR8">8</CitationRef>], which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of [<CitationRef CitationID="CR8">8</CitationRef>, <CitationRef CitationID="CR14">14</CitationRef>], as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proven.</p>

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Singular Flows with Time-Varying Weights

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月17日

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  • Immanuel Ben-Porat,
  • José A. Carrillo,
  • Pierre-Emmanuel Jabin

摘要

We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty [14] and Bresch-Jabin-Wang [8], which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of [8, 14], as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proven.