Many-particle limit for a system of interaction equations driven by\n Newtonian potentials

2020/08/25 by Marco Di Francesco, Di Francesco, Marco, Antonio Esposito +3 · 1 citation
Materials Science · Mathematics · Medicine · #35A35 #35F55. Secondary: 82C22 #35Q70 #35R09 #Analysis of PDEs (math.AP) #Blood properties and coagulation #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Material Dynamics and Properties #Primary: 35A24

paper · pdf · doi:10.48550/arxiv.2008.11106

openalex publication_date 2020/08/25 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider a discrete particle system of two species coupled through\nnonlocal interactions driven by the one-dimensional Newtonian potential, with\nrepulsive self-interaction and attractive cross-interaction. After providing a\nsuitable existence theory in a finite-dimensional framework, we explore the\nbehaviour of the particle system in case of collisions and analyse the\nbehaviour of the solutions with initial data featuring particle clusters.\nSubsequently, we prove that the empirical measure associated to the particle\nsystem converges to the unique 2-Wasserstein gradient flow solution of a system\nof two partial differential equations (PDEs) with nonlocal interaction terms in\na proper measure sense. The latter result uses uniform estimates of the\nL^m-norms of a piecewise constant reconstruction of the density using the\nparticle trajectories.\n

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