The Mean-Field Limit for a Regularized Vlasov-Maxwell Dynamics |
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Authors: | Email author" target="_blank">Fran?ois?GolseEmail author |
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Institution: | 1.Ecole Polytechnique,Centre de Mathématiques Laurent Schwartz,Palaiseau Cedex,France;2.Université Paris Diderot-Paris 7, Laboratoire J.-L. Lions,Paris Cedex 05,France |
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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
Commun Math Phys 56:101–113, 1977] and Dobrushin Func Anal Appl 13:115–123, 1979] 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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Keywords: | |
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