2018/03/11 by Samir Salem, Salem, Samir
Mathematics · Physics and Astronomy · #Gas Dynamics and Kinetic Theory #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1803.04017
In this paper we consider a system of N particles on the real line evolving according to Newton's law, interacting through a singular (repulsive) force deriving from the potential \frac|x|1-α1-α with α∈ (0,1/8) and Brownian force. Thanks to the entropy dissipation along the Liouville equation associated to this particles system and a control of the mechanic energy, we establish a quantitative estimate which enables to conclude to a convergence/consistency the particles system toward the limiting Vlasov-Fokker-Planck equation with singular force.