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arXiv · 1111.0423

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

Nicolas Lerner·Yoshinori Morimoto·Karel Pravda-Starov·Chao-Jiang Xu
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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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Nicolas Lerner, Yoshinori Morimoto, Karel Pravda-Starov, Chao-Jiang Xu. 2011-11-02. Spectral and phase space analysis of the linearized non-cutoff Kac collision operator. https://arxiv.org/abs/1111.0423

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