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The classical limit of the relativistic Vlasov-Maxwell system. (English) Zbl 0597.35109

This paper starts by showing that for smooth Cauchy data, classical solutions exist for the relativistic Vlasov-Maxwell system of equations on a time interval independent of the speed of light c. An integral representation for the electric and magnetic fields in the relativistic Vlasov-Maxwell system of equations is then used to find conditions under which solutions of this system converge pointwise to solutions of the non-relativistic Vlasov-Poisson system. The convergence is shown to be at the asymptotic rate of 1/c as c tends to infinity.
Reviewer: A.Jeffrey

MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35C15 Integral representations of solutions to PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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