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Spectral and phase space analysis of the linearized non-cutoff Kac collision operator

Authors
  • Lerner, Nicolas
  • Morimoto, Yoshinori
  • Pravda-Starov, Karel
  • Xu, Chao-Jiang
Type
Preprint
Publication Date
Apr 04, 2012
Submission Date
Nov 02, 2011
Identifiers
arXiv ID: 1111.0423
Source
arXiv
License
Yellow
External links

Abstract

The non-cutoff Kac operator is a kinetic model for the non-cutoff radially symmetric Boltzmann operator. For Maxwellian molecules, the linearization of the non-cutoff Kac operator around a Maxwellian distribution is shown to be a function of the harmonic oscillator, to be diagonal in the Hermite basis and to be essentially a fractional power of the harmonic oscillator. This linearized operator is a pseudodifferential operator, and we provide a complete asymptotic expansion for its symbol in a class enjoying a nice symbolic calculus. Related results for the linearized non-cutoff radially symmetric Boltzmann operator are also proven.

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