2011/11/07 by François Golse · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Distribution (mathematics) #Dynamics (music) #Electromagnetic field #Gas Dynamics and Kinetic Theory #Kinetic energy #Limit (mathematics) #Maxwell's equations #Momentum (technical analysis) #Relativistic dynamics #Stability (learning theory) #Statistical Mechanics and Entropy #Thermoelastic and Magnetoelastic Phenomena #Work (physics) #math-ph #math.AP #math.MP #msc:35Q61 #msc:35Q83 #msc:82C22 #msc:82D10
paper · pdf · doi:10.1007/s00220-011-1377-8
published as Comm. in Math. Phys. 310 (2012), 789-816 · 34 pages
arxiv created 2011/11/07 · openalex publication_date 2012/01/18 · arxiv updated 2012/07/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.