Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials

Details Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials

2006-07-21

arxiv.org/abs/math/0607532v1

Revista Matem\'{a}tica Iberoamericana 21 (2005) 819-841

Mathematics

Analysis of PDEs

22 pages

Scientific paper

This paper deals with explicit spectral gap estimates 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 deduce explicit spectral gap estimates for the linearized Landau operator with hard potentials.

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