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The mean-field limit for a regularized Vlasov-Maxwell dynamics. (English) Zbl 1251.82037
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 W. Braun and K. Hepp [Commun. Math. Phys. 56, No. 2, 101–113 (1977; Zbl 1155.81383)] and of R. L. Dobrushin [Funct. Anal. Appl. 13, 115–123 (1979; Zbl 0422.35068)] 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 the 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.

MSC:
82C22 Interacting particle systems in time-dependent statistical mechanics
35Q83 Vlasov equations
35Q61 Maxwell equations
82D10 Statistical mechanics of plasmas
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