Local existence of solutions of the vlasov‐maxwell equations and convergence to the vlasov‐poisson equations for infinite light velocity

摘要

AbstractWe prove the local existence of smooth solutions for the Vlasov‐Maxwell equations in three space variables. The existence time for such solutions is independent of the light velocityc. 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 velocitycgoes to