Growth estimates and uniform decay for a collisionless plasma
The classical Vlasov-Poisson system in three space dimensions and its asymptotic solutions are considered in the electrostatic case. For smooth solutions starting from compactly supported initial data, an estimate on velocities is derived, showing an upper bound with a growth rate no larger than \((t\ln t)^{6/25}\), where \(t\) denotes the time variable. As a consequence, a decay estimate is obtained for the electric field in the \(L^\infty\) norm.
scientific article; zbMATH DE number 5925673