The Mean Field Kinetic Equation for Interacting Particle Systems with Non-Lipschitz Force

2017/09/08 by Yin, Qitao, Chen, Li, Göttlich, Simone
#35Q83 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.02686

Abstract

In this paper, we prove the global existence of the weak solution to the mean field kinetic equation derived from the N-particle Newtonian system. For L¹∩ L^∞ initial data, the solvability of the mean field kinetic equation can be obtained by using uniform estimates and compactness arguments while the difficulties arising from the non-local non-linear interaction are tackled appropriately using the Aubin-Lions compact embedding theorem.

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