On Global Classical Limit of the (Relativistic) Vlasov–Maxwell System

Abstract

Abstract It is shown that solutions of the (relativistic) Vlasov–Maxwell system converge pointwise to solutions of the Vlasov–Poisson system globally in time at the asymptotic rate of $$c^{-1},$$ c - 1 , as the light speed c tends to infinity, which extends the results of Asano and Ukai (Stud Math Appl 18:369–383, 1986), Degond (Math Methods Appl Sci 8:533–558, 1986) and Schaeffer (Commun Math Phys 104:403–421, 1986). The analysis relies on the method of Glassey and Strauss (Commun Math Phys 113:191–208, 1987) and Schaeffer (Commun Math Phys 104:403–421, 1986).