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

被引：19

作者：

Lerner, N. ^{[1
]}

Morimoto, Y. ^{[2
]}

Pravda-Starov, K. ^{[3
]}

Xu, C. -J. ^{[4
,5
]}

机构：

[1] Univ Paris 06, Inst Math Jussieu, F-75252 Paris 05, France

[2] Kyoto Univ, Grad Sch Human & Environm Studies, Kyoto 6068501, Japan

[3] Univ Cergy Pontoise, CNRS, Dept Math, UMR 8088, F-95000 Cergy Pontoise, France

[4] Wuhan Univ, Sch Math, Wuhan 430072, Peoples R China

[5] Univ Rouen, CNRS, Dept Math, UMR 6085, F-76801 St Etienne, France

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2013年 / 100卷 / 06期

基金：

美国国家科学基金会; 日本学术振兴会;

关键词：

Non-cutoff Kac equation; Non-cutoff Boltzmann equation; Spectral analysis; Microlocal analysis; BOLTZMANN-EQUATION; ANGULAR CUTOFF; KINETIC-EQUATIONS;

D O I：

10.1016/j.matpur.2013.03.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：832 / 867

页数：36

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