Journal of Statistical Physics

, 89:751

On boltzmann equations and fokker—planck asymptotics: Influence of grazing collisions

  • T. Goudon

DOI: 10.1007/BF02765543

Cite this article as:
Goudon, T. J Stat Phys (1997) 89: 751. doi:10.1007/BF02765543


In this paper, we are interested in the influence of grazing collisions, with deflection angle near π/2, in the space-homogeneous Boltzmann equation. We consider collision kernels given by inverse-sth-power force laws, and we deal with general initial data with bounded mass, energy, and entropy. First, once a suitable weak formulation is defined, we prove the existence of solutions of the spatially homogeneous Boltzmann equation, without angular cutoff assumption on the collision kernel, fors ≥ 7/3. Next, the convergence of these solutions to solutions of the Landau-Fokker-Planck equation is studied when the collision kernel concentrates around the value π/2. For very soft interactions, 2<s<7/3, the existence of weak solutions is discussed concerning the Boltzmann equation perturbed by a diffusion term

Key Words

Kinetic equationhomogeneous Boltzmann equationLandau-Fokker-Planck equationgrazing collisions

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • T. Goudon
    • 1
  1. 1.Mathématiques Appliquées de BordeauxCNRS-Université Bordeaux ITalence CedexFrance