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About the regularizing properties of the non-cut-off Kac equation. (English) Zbl 0827.76081

Summary: We prove that under suitable assumptions, the solution of the spatially homogeneous non-cut-off Kac equation (or of the spatially homogeneous non cut-off two-dimensional Boltzmann equation with Maxwellian molecules in the radial case) becomes very regular with respect to the velocity variable as soon as the time is strictly positive.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82D05 Statistical mechanics of gases
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