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.
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Funding
National Key R&D Program of China(2021YFA1002800)
National Natural Science Foundation of China(No.12171009)
Young Elite Scientists Sponsorship Program by CAST(No.YESS20200028)
Fundamental Research Funds for the Central Universities, Peking University
RIGHTS & PERMISSIONS
Peking University
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