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<p>We derive the quantitative estimates of propagation of chaos for the large interacting particle systems in terms of the relative entropy between the joint law of the particles and the tensorized law of the mean-field PDE. We resolve this problem for the first time for the viscous vortex model that approximates the 2D Navier–Stokes equation in the vorticity formulation on the whole space. We obtain as key tools the Li–Yau-type estimates and Hamilton-type heat kernel estimates for the 2D Navier–Stokes equation on the whole space.</p>

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Quantitative Propagation of Chaos for 2D Viscous Vortex Model on the Whole Space

  • 期刊论文

  • 发表日期：

    2026年3月18日

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  • Xuanrui Feng,
  • Zhenfu Wang

摘要

We derive the quantitative estimates of propagation of chaos for the large interacting particle systems in terms of the relative entropy between the joint law of the particles and the tensorized law of the mean-field PDE. We resolve this problem for the first time for the viscous vortex model that approximates the 2D Navier–Stokes equation in the vorticity formulation on the whole space. We obtain as key tools the Li–Yau-type estimates and Hamilton-type heat kernel estimates for the 2D Navier–Stokes equation on the whole space.