ON THE LAGRANGIAN STRUCTURE OF VLASOV-MAXWELL EQUATIONS FOR ELECTROMAGNETIC FIELD WITH BOUNDED VARIATION

We study the Lagrangian structure of Vlasov-Maxwell equations. We show that for sufficiently regular initial conditions, renormalized solutions of these systems are Lagrangian and that these notions of solution, in fact, coincide. As a consequence, finite-energy solutions are shown to be transported by a global flow. These results extend to our setting those obtained by Ambrosio, Colombo, and Figalli [3] for the Vlasov-Poisson system and by the first author and Marcon for relativistic Vlasov systems [5]; here, we analyze the electromagnetic fields with bounded variation under Maxwell equations.