Propagation of Chaos for N Particle Models with Singular Potentials
Time: 2022-03-21
Published By: He Liu
Speaker(s): Rong Yang (Beijing University of Technology)
Time: 16:00-17:30 March 24, 2022
Venue: Room 29, Quan Zhai, BICMR
In this talk, we first consider an N-particle interacting system with the Newtonian potential aggregation and Brownian motions. Assuming that the initial data are i.i.d. with a common probability density function satisfying some conditions, we prove the propagation of chaos for this interacting system with a cut-off parameter by the coupling method. Then, we investigate a system of N-particle system with the Coulomb interactions. We prove that there exists a unique global strong solution for this interacting particle system in any dimension and prove in the 2 dimensioal case a propagation of chaos result without any cut-off. Finally, we give the well-posedness result of a second-order SDEs describing an N-particle system interacting via the Coulomb interaction.
