Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium

Joackim Bernier (1, 2) , Michel Mehrenberger (3)

1 MINGUS - Multi-scale numerical geometric schemes
2 IRMAR - Institut de Recherche Mathématique de Rennes
3 I2M - Institut de Mathématiques de Marseille

The asymptotic behavior of the solutions of the second order linearized Vlasov-Poisson system around homogeneous equilibria is derived. It provides a fine description of some nonlinear and multidimensional phenomena such as the existence of Best frequencies. Numerical results for the 1D×1D and 2D×2D Vlasov-Poisson system illustrate the effectiveness of this approach.

Mots clés: Vlasov-Poisson; Best frequency; Landau damping; Dispersion relations; Laplace transform

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Joackim Bernier, Michel Mehrenberger. Long-time behavior of second order linearized Vlasov-Poisson equations near a homogeneous equilibrium. Kinetic and Related Models , 2020, 13 (1), pp.129-168. ⟨10.3934/krm.2020005⟩. ⟨hal-02070138v3⟩