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Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials. (English) Zbl 1092.76057

Summary: This paper deals with explicit spectral gap estiamtes for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl’s theorem, and thus does not require Grad’s splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator can be expressed as the limit of the Boltzmann operator as collisions become grazing in order to derive explicit spectral gap estimates for the linearized Landau operator with hard potentials.

MSC:

76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82B40 Kinetic theory of gases in equilibrium statistical mechanics
82D05 Statistical mechanics of gases
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