北航学术报告

---分析、偏微分方程与动力系统讨论班(2026春季第14讲)

Singular Mean-Field Limits and Collisions for Interacting Particle Systems

Quoc Hung Nguyen（中国科学院数学与系统科学研究院）

时间：2026年08月12日（周三）下午14:00-14:40

地点：北航学院路老主楼 主410

摘要: We consider large systems of interacting particles driven by singular forces of the form F(x,y)~|x-y|^{-s}, allowing non-gradient, non-symmetric, and attractive interactions. We study the convergence of the empirical measure of the particle system toward the corresponding mean-field equation, including regimes in which particle collisions may occur.

The main tool is a multiscale distance based on heat regularization, which measures the discrepancy between the empirical measure and the limiting density simultaneously at several spatial scales. This allows us to treat Coulomb, sub-Coulomb, and super-Coulomb singularities and to obtain quantitative convergence estimates. In a weaker dual topology, we also recover the optimal convergence rate of order \(N^{-1/d}\). For attractive interactions, we construct configurations exhibiting finite-time collisions and determine the corresponding collision time scales and rates. The analysis combines kernel commutator estimates, multiscale bootstrap arguments, dual transport estimates, and a careful treatment of weak particle continuations beyond collisions. This is joint work with Sylvia Serfaty.

报告人简介: Quoc Hung Nguyen is an Associate Professor at the Academy of Mathematics and Systems Science (AMSS). His research interests lie in partial differential equations (PDEs) arising from fluid dynamics and kinetic theory, regularity theory for elliptic and parabolic equations, and nonlinear potential theory. He has published several papers in leading journals, including Communications on Pure and Applied Mathematics (CPAM), Journal of the European Mathematical Society (JEMS), Memoirs of the American Mathematical Society ( MEM of AMS), Archive for Rational Mechanics and Analysis (ARMA), Communications in Mathematical Physics (CMP), and Advances in Mathematics (AIM).

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