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

DOI10.1016/j.matpur.2013.03.005zbMath1285.35061arXiv1111.0423OpenAlexW2962897537MaRDI QIDQ386266

Karel Pravda-Starov, Nicolas Lerner, Yoshinori Morimoto, Chao-Jiang Xu

Publication date: 9 December 2013

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.0423

zbMATH Keywords

convergenceasymptotic expansionspectral analysiskinetic theorycollisionmicrolocal analysisgasesEuclidian normforce-free particlesKac operatorMaxwell distributionnon-cutoff Boltzmann equationnon-cutoff Kac equation

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Fractional partial differential equations (35R11) Boltzmann equations (35Q20)

Related Items

Sharp regularity properties for the non-cutoff spatially homogeneous Boltzmann equation, Shubin regularity for the radially symmetric spatially homogeneous Boltzmann equation with Debye-Yukawa potential, \(L^p\)-maximal hypoelliptic regularity of nonlocal kinetic Fokker-Planck operators, Gelfand-Shilov Smoothing Effect for the Radially Symmetric Spatially Homogeneous Landau Equation under the Hard Potential γ=2, Global Solution for the Spatially Inhomogeneous Non-cutoff Kac Equation, Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff, Smoothing effect and Cauchy problem for radially symmetric homogeneous Boltzmann equation with Debye-Yukawa potential of Shubin class initial datum, Metastability results for a class of linear Boltzmann equations, Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff, The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space, The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand-Shilov smoothing effect, Sharp regularity and Cauchy problem of the spatially homogeneous Boltzmann equation with Debye-Yukawa potential, Gelfand-Shilov and Gevrey smoothing effect of the Cauchy problem for Fokker-Planck equation, Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation

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