Landau damping on the torus for the Vlasov-Poisson system with massless electrons

2022/09/10 by Gagnebin, Antoine, Iacobelli, Mikaela
#35Q83 #76F25 #82C99 #82D10 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2209.04676

Abstract

This paper studies the nonlinear Landau damping on the torus \mathbbT^d for the Vlasov-Poisson system with massless electrons (VPME). We consider solutions with analytic or Gevrey (γ> 1/3) initial data, close to a homogeneous equilibrium satisfying a Penrose stability condition. We show that for such solutions, the corresponding density and force field decay exponentially fast as time goes to infinity. This work extends the results for Vlasov-Poisson on the torus to the case of ions and, more generally, to arbitrary analytic nonlinear couplings.

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