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

Abstract

We are concerned with the global well-posedness of the non-relativistic Vlasov–Darwin system with generalized variables approach in three dimensions. We obtain the global existence and uniqueness of classical solutions for the perturbation of global solutions with specified decay conditions. And generalizing the result of the quasi-spherical-symmetry case, we prove the existence and uniqueness of the global classical solution of the system when initial data sufficiently closes to a fixed spherically symmetric function. Moreover, we obtain asymptotic behavior for the Darwin potentials in both cases.