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arXiv · 2402.04695

A duality method for mean-field limits with singular interactions

Didier Bresch·Mitia Duerinckx·Pierre-Emmanuel Jabin
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Abstract

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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Didier Bresch, Mitia Duerinckx, Pierre-Emmanuel Jabin. 2024-02-07. A duality method for mean-field limits with singular interactions. https://arxiv.org/abs/2402.04695

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