GLOBAL SOLUTIONS FOR THE ONE-DIMENSIONAL VLASOV–MAXWELL SYSTEM FOR LASER-PLASMA INTERACTION

Abstract

We analyze a reduced 1D Vlasov–Maxwell system introduced recently in the physical literature for studying laser-plasma interaction. This system can be seen as a standard Vlasov equation in which the field is split into two terms: an electrostatic field obtained from Poisson's equation and a vector potential term satisfying a nonlinear wave equation. Both nonlinearities in the Poisson and wave equations are due to the coupling with the Vlasov equation through the charge density. We show global existence of weak solutions in the nonrelativistic case, and global existence of characteristic solutions in the quasi-relativistic case. Moreover, these solutions are uniquely characterized as fixed points of a certain operator. We also find a global energy functional for the system allowing us to obtain Lp-nonlinear stability of some particular equilibria in the periodic setting.