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

2023/10/08 by Xuanrui Feng, Zhenfu Wang, Feng, Xuanrui +1 · 4 citations
Physics and Astronomy · Mathematics · Engineering · #Cosmology and Gravitation Theories #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2310.05156

Abstract

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 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 2D Navier-Stokes in the whole space.

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