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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