Landau Damping for the Linearized Vlasov Poisson Equation in a Weakly Collisional Regime

In this paper, we consider the linearized Vlasov–Poisson equation around an homogeneous Maxwellian equilibrium in a weakly collisional regime: there is a parameter ({varepsilon }) 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 ({varepsilon }) as it goes to 0.