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The grazing collision asymptotics of the non cut-off Kac equation. (English) Zbl 0912.76081

Summary: We investigate the non cut-off Kac equation when the cross-section is concentrating on grazing collisions. We prove that this process leads to the one-dimensional Fokker-Planck equation, and that, under suitable regularity of the initial data, the convergence is uniform in time.

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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References:

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