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On the homogeneous Boltzmann equation and its relation to the Landau-Fokker-Planck equation: Influence of grazing collisions. (Sur l’équation de Boltzmann homogène et sa relation avec l’équation de Landau-Fokker-Planck: Influence des collisions rasantes.) (French. Abridged English version) Zbl 0882.76079

Summary: We prove the existence of weak solutions of the spatially homogeneous Boltzmann equation without angular cut-off assumption for inverse \(s^{th}\) power molecules with \(s\geq {7\over 3}\), and for general initial data with bounded mass, kinetic energy and entropy. Next, we show the convergence of these solutions to solutions of the Landau-Fokker-Planck equation when the collision kernel concentrates around the value \({\pi \over 2}\).

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
45K05 Integro-partial differential equations
82B40 Kinetic theory of gases in equilibrium statistical mechanics
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