On global classical solutions of the three dimensional non-relativistic Vlasov–Darwin System

We study the Cauchy problem of the relativistic Vlasov-Darwin system with generalized variables proposed by Sospedra-Alfonso et al. [“Global classical solutions of the relativistic Vlasov-Darwin system with small Cauchy data: the generalized variables approach,” Arch. Ration. Mech. Anal. 205, 827-869 (2012)]. We prove global existence of a non-negative classical solution to the Cauchy problem in three space variables under small perturbation of the initial datum, and as a consequence, we obtain that nearly spherically symmetric solutions with required regularity exist globally in time.