Moment propagation of a Vlasov-Poisson system for ions flow in the quasi-neutral regime

In light of recent work in the global well-posedness of solutions for an ionic Vlasov-Poisson system, as demonstrated by Griffin-Pickering and Iacobelli, the current work focuses on the moment propagation of the corresponding system in quasi-neutral regime. Such moment propagation result relies on an estimate of $Q_{\ast }(t)=\mathrm{\mid }V(t;0,x,v)-V(0;0,x,v)\mathrm{\mid }$, where $V(s;t,x,v)$ represents the solution of the characteristic ordinary differential equation associated with the Vlasov-Poisson system.