SYMETRIZATION OF VLASOV-POISSON EQUATIONS

Bruno Després (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We detail the spectrum of the linearized Vlasov-Poisson equation, and construct an original integro-differential operator which is related to the eigenstructure. It gives a new representa- tion formula for the electric field, and yields new estimates for the linear Landau damping. Then we apply the technique to a problem with a dependence to the Debye length, and show weaker damping for small Debye length. A non linear variant of the main quadratic framework is finally discussed.

Mots clés: Vlasov-Poisson equation; Landau damping; integro-differential operator; Debye length

Domaines: Physique mathématique [math-ph]

Bruno Després. SYMETRIZATION OF VLASOV-POISSON EQUATIONS. SIAM Journal on Mathematical Analysis, 2014, 46 (4), pp.2554-2580. ⟨hal-00837486⟩