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On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations

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Abstract

This paper deals with the spatially homogeneous Boltzmann equation when grazing collisions are involved.We study in a unified setting the Boltzmann equation without cut-off, the Fokker-Planck-Landau equation, and the asymptotics of grazing collisions for a very broad class of potentials; in particular, we are able to derive rigorously the Landau equation for the Coulomb potential. In order to do so, we introduce a new definition of weak solutions, based on entropy production.

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  1. Ecole Normale Supérieure, DMI 45 rue d’Ulm, F-75230, Paris Cedex 05, France

    Cédric Villani

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  1. Cédric Villani
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Villani, C. On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations. Arch Rational Mech Anal 143, 273–307 (1998). https://doi.org/10.1007/s002050050106

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