The relativistic Vlasov Maxwell equations for strongly magnetized plasmas

Christophe Cheverry (1) , Slim Ibrahim (2, 3)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 EDP
3 UVIC - University of Victoria [Canada]

An important challenge in plasma physics is to determine whether ionized gases can be confined by strong magnetic fields. After properly formulating the model, this question leads to a penalized version of the Relativistic Vlasov Maxwell system, marked by the role of a singular factor ε −1 corresponding to the inverse of a cyclotron frequency. In this paper, we prove in this context the existence of classical C 1-solutions for a time independent of ε. We also investigate the stability of these smooth solutions.

Mots clés: Kinetic equations; Vlasov-Maxwell system; Magnetized plasmas; Lifespan of classical solutions; Momentum support condition; Energy estimates

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Cheverry, Slim Ibrahim. The relativistic Vlasov Maxwell equations for strongly magnetized plasmas. Communications in Mathematical Sciences, In press. ⟨hal-02090322⟩