The grazing collision limit for the Boltzmann–Lorentz model

Article type: Research Article

Authors: Buet, C. | Cordier, S. | Lucquin‐Desreux, B.

Affiliations: CEA/DRIR, B.P. 12, 91 680 Bruyères‐Le‐Châtel, France E‐mail: buet@bruyeres.cea.fr | Laboratoire d'Analyse Numérique, UMR CNRS 7598, Université Pierre et Marie Curie, Boîte courrier 187, 75 252 Paris cedex 05, France E‐mail: cordier@ann.jussieu.fr; lucquin@ann.jussieu.fr

Abstract: The Lorentz operators are derived from either Boltzmann or Fokker–Planck collisions operators when considering a mixture of species with disparate masses [8]. The Fokker–Planck operator is the so called “grazing collision limit” of the Boltzmann operator as proved in [1,12,7]. In our simpler case, we improve the results by proving uniform in time convergence and by controling the speed of the trend to equilibrium. The results are based on a spectral analysis of the operators which share the same basis of eigenfunctions.

Journal: Asymptotic Analysis, vol. 25, no. 2, pp. 93-107, 2001