The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics

François Golse (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions

The present work establishes the mean-field limit of a N-particle system towards a regularized variant of the relativistic Vlasov-Maxwell system, following the work of Braun-Hepp [Comm. in Math. Phys. 56 (1977), 101--113] and Dobrushin [Func. Anal. Appl. 13 (1979), 115--123] for the Vlasov-Poisson system. The main ingredients in the analysis of this system are (a) a kinetic formulation of the Maxwell equations in terms of a distribution of electromagnetic potential in the momentum variable, (b) a regularization procedure for which an analogue of the total energy --- i.e. the kinetic energy of the particles plus the energy of the electromagnetic field --- is conserved and (c) an analogue of Dobrushin's stability estimate for the Monge-Kantorovich-Rubinstein distance between two solutions of the regularized Vlasov-Poisson dynamics adapted to retarded potentials.

Mots clés: Mean-field limit; Vlasov-Maxwell system; Lienard-Wiechert potential; Monge-Kantorovich-Rubinstein distance

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

François Golse. The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics. Communications in Mathematical Physics, 2012, 310 (no. 3), pp.789-816. ⟨10.1007/s00220-011-1377-8⟩. ⟨hal-00545569v2⟩