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Quantitative mean-field limits for repulsive Coulomb flows at bounded density and Riesz weak--strong stability — arXiv:2608.16655

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.16655
License (as archived): CC0-1.0
Archived: 2026-10-18T20:25:44.041Z
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Quantitative mean-field limits for repulsive Coulomb flows at bounded density and Riesz weak--strong stability — arXiv:2608.16655 — arXiv (en), https://arxiv.org/abs/2608.16655 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0ca8c2ef91c2 (Metraipolis archive dc_0ca8c2ef91c2, sha256 2e29174a4c6ecc1d2ba1b919b4b73234dcd988076087a29d88bab750dd1d5da5)

BibTeX

@misc{dc0ca8c2ef91c2,
  title = {Quantitative mean-field limits for repulsive Coulomb flows at bounded density and Riesz weak--strong stability — arXiv:2608.16655},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.16655},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0ca8c2ef91c2; sha256 2e29174a4c6ecc1d2ba1b919b4b73234dcd988076087a29d88bab750dd1d5da5},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.16655. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We establish quantitative mean-field convergence and propagation of chaos for repulsive Coulomb gradient flows at the bounded-density regularity of the limiting equation. The argument couples the dissipative modulated-energy identity with the normalized quadratic transport cost of the full $N$-particle law. The remaining negative mean-square force-error term is used through an exact completion of squares after mollification: the non-Lipschitz remainder is absorbed by this negative term, while a sharp first-order commutator estimate is applied to the mollified Lipschitz field. For the Coulomb equation, the sharp $L^\infty$ decay gives the density envelope $m(t)=\|\rho_0\|_{L^\infty}/(1+t\|\rho_0\|_{L^\infty})$. A density-adapted transport weight and mollification scale $m(t)^{-1/d}$ yield an Osgood comparison. Thus, for every $d\ge2$ and $\rho_0\in\mathcal P_2(\mathbb R^d)\cap L^\infty(\mathbb R^d)$, we obtain quantitative comparison with the global bounded-density Coulomb solution on every prescribed finite interval. For tensorized initial data, the normalized squared Wasserstein distance of the full $N$-particle law, the expected modulated energy, and the time-integrated mean-square force error are bounded by $N^{-2\gamma_{T,d}/d}$ for $d\ge3$ and $((1+\log N)/N)^{\gamma_{T,2}}$ for $d=2$, where $\gamma_{T,d}=(1+T\|\rho_0\|_{L^\infty})^{-c_d}$. For $d-2<s<d$, we also prove Riesz weak--strong stability for prescribed reference solutions in $L^\infty(0,T;B^{s-d+2}_{\infty,q})$, with Gronwall, Bihari, and Osgood comparisons according to $q$, together with uniqueness in the stated Besov class. Finally, an outlier construction separates modulated-energy convergence and Kac chaos from normalized Wasserstein convergence of the full $N$-particle law.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-18 in math.PR).
Categorie arXiv: Analysis of PDEs (math.AP) ; Probability (math.PR).
Pagina del lavoro: https://arxiv.org/abs/2608.16655 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T19:45:36.400Z dalla pagina https://arxiv.org/catchup/math.PR/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).