Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime

Isabelle Tristani (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

In this paper, we consider the linearized Vlasov-Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter $\eps$ in front of the collision operator which will tend to $0$. Moreover, we study two cases of collision operators, linear Boltzmann and Fokker-Planck. We prove a result of Landau damping for those equations in Sobolev spaces uniformly with respect to the collision parameter $\eps$ as it goes to $0$.

Mots clés: Landau damping; Vlasov-Poisson equation; Fokker-Planck operator; linear Boltzmann operator

Domaines: Equations aux dérivées partielles [math.AP]

Isabelle Tristani. Landau damping for the linearized Vlasov Poisson equation in a weakly collisional regime . 2016. ⟨hal-01292023v2⟩