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

Abstract : 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.
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Contributor : François Golse <>
Submitted on : Monday, November 7, 2011 - 2:30:12 AM
Last modification on : Monday, December 14, 2020 - 9:41:37 AM
Long-term archiving on: : Wednesday, February 8, 2012 - 2:21:53 AM


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



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