Sharp uniform-in-time mean-field convergence for singular periodic Riesz flows

  • Antonin Chodron de Courcel

    Institut des Hautes Études Scientifiques, Université Paris-Saclay, CNRS, Bures-sur-Yvette, France
  • Matthew Rosenzweig

    Carnegie Mellon University, Pittsburgh, USA
  • Sylvia Serfaty

    Courant Institute of Mathematical Sciences, New York, USA
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Abstract

We consider conservative and gradient flows for -particle Riesz energies with mean-field scaling on the torus , for , and with thermal noise of McKean–Vlasov type. We prove global well-posedness and relaxation to equilibrium rates for the limiting PDE. Combining these relaxation rates with the modulated free energy of Bresch et al. (2019, 2019–2020, 2020) and recent sharp functional inequalities of the last two named authors for variations of Riesz modulated energies along a transport, we prove uniform-in-time mean-field convergence in the gradient case with a rate which is sharp for the modulated energy pseudo-distance. For gradient dynamics, this completes in the periodic case the range not addressed by the previous work Rosenzweig and Serfaty (2023). We also combine our relaxation estimates with the relative entropy approach of Jabin and Wang (2018) for so-called kernels, giving a proof of uniform-in-time propagation of chaos alternative to Guillin et al. (2021).

Cite this article

Antonin Chodron de Courcel, Matthew Rosenzweig, Sylvia Serfaty, Sharp uniform-in-time mean-field convergence for singular periodic Riesz flows. Ann. Inst. H. Poincaré C Anal. Non Linéaire (2023), published online first

DOI 10.4171/AIHPC/105