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

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Abstract

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

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  1. Mathématiques Appliquées de Bordeaux, CNRS-Université Bordeaux I, F-33405, Talence Cedex, France

    T. Goudon

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Goudon, T. On boltzmann equations and fokker—planck asymptotics: Influence of grazing collisions. J Stat Phys 89, 751–776 (1997). https://doi.org/10.1007/BF02765543

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  • DOI: https://doi.org/10.1007/BF02765543

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