CONSTRUCTION OF MOLLER WAVE OPERATORS FOR VLASOV EQUATIONS LINEARIZED AROUND BOLTZMANNIAN STATES *
Construction des opérateurs de Moller Pour l'équation de Vlasov
Résumé
We detail a possible construction of the Moller wave operators for linear Vlasov-Poisson and Vlasov-Ampere equations. This is based on an explicit and detailed calculation of the eigenstructure. A simple non homogeneous case is detailed. We finally show that, for the homogeneous case, the Morrison transform is exactly the Moller wave operator. 1. Introduction. This work is a extension of a previous one [6] on the linearized Vlasov-Poisson or Vlasov-Ampere equation and is dedicated to new connections between Moller wave operators (in the context of the abstract theory of scattering [15, 19, 13, 32]) for general homogeneous or non homogeneous states and the Morrison integral transform [24, 25]. It yields an alternative to the standard Hamiltonian framework privileged in Morrison works. Indeed it seems that the abstract scattering theory per se has never been adapted to the study of linearized Vlasov-Poisson equation, or more precisely, the fact that Moller wave operators give a proof of linear Landau damping has never been explicitly formulated [27]. The associated algebra gives some tracks in the direction of a proof of linear Landau damping [18, 27] for non homogeneous states [28, 3]. In particular we rigorously derive an integral equation which appears to be fundamental for the definition of Moller operators for non homogeneous Boltzmannian states. The model problem is a Vlasov-Amp ere equation in dimension 1+1
Nous construisons les opérateurs de Moller pour les équations de Vlasov linéarisées.
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