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A duality method for mean-field limits with singular interactions

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arxiv 2402.04695 v2 pith:KXQTV6YS submitted 2024-02-07 math.AP math-phmath.MP

Didier Bresch , Mitia Duerinckx , Pierre-Emmanuel Jabin This is my paper · ORCID
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keywords approachmean-fieldallowsdualityinteractionslimitssingularsystems
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We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. In case of first-order systems, it allows to recover in particular the mean-field limit to the 2d Euler and Navier-Stokes equations. The approach also provides convergence rates.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Singular mean-field limits via a multiscale mollification metric

    math.AP 2026-07 accept novelty 8.0 of 10

    Multiscale mollification by heat kernels yields quantitative mean-field limits for singular particle systems (sub-Coulomb global, Coulomb short-time in d≥3, super-Coulomb N-dependent), optimal by collision examples.

  2. Kac's Program for the Landau Equation

    math.AP 2025-06 conditional novelty 8.0 of 10

    The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L...

  3. Quantitative Estimates for Mean-Field Limits and Correlation Functions through a Duality Framework

    math.AP 2026-05 unverdicted novelty 6.0 of 10

    It proves O(N^{-1/2}) and O(N^{-1}) convergence rates for deterministic Vlasov marginals and O(N^{-k/2}) bounds on direct cumulants via an iterated dual-cumulant hierarchy.

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