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Local existence of solutions of the Vlasov-Maxwell equations and convergence to the Vlasov-Poisson equations for infinite light velocity. (English) Zbl 0619.35088
We prove the local existence of smooth solutions for the Vlasov-Maxwell equations in three space variables. The existence time for such solutions is independant of the light velocity c. Then we derive regularity results for both the Vlasov-Poisson and the Vlasov-Maxwell equations. The last part of the paper is devoted to a proof of weak and strong convergence of the Vlasov-Maxwell equations towards the Vlasov-Poisson equations, when the light velocity c goes to infinity.

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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