Global solutions for the one-dimensional Vlasov-Maxwell system for Laser-Plasma interaction

José A. Carrillo (1) , Simon Labrunie (2)

1 ICREA - Institució Catalana de Recerca i Estudis Avançats = Catalan Institution for Research and Advanced Studies
2 CALVI - Scientific computation and visualization

We analyse 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 in 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 non-relativistic case, and global existence of characteristic solutions in the quasi-relativistic case. Moreover, these solutions are uniquely characterised as fixed points of a certain operator. We also find a global energy functional for the system allowing us to obtain $L^p$-nonlinear stability of some particular equilibria in the periodic setting.

Mots clés: nonlinear stability; Kinetic equations; Vlasov--Maxwell system; existence and uniqueness of solutions

Domaines: Equations aux dérivées partielles [math.AP]

José A. Carrillo, Simon Labrunie. Global solutions for the one-dimensional Vlasov-Maxwell system for Laser-Plasma interaction. Mathematical Models and Methods in Applied Sciences, 2006, 16 (1), pp.19-57. ⟨10.1142/S0218202506001042⟩. ⟨hal-00094327⟩