Spectrum structure and behaviors of the Vlasov-Maxwell-Boltzmann systems

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)595-669
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume48
Issue number1
Online published16 Feb 2016
Publication statusPublished - 2016

Abstract


The spectrum structures and behaviors of the Vlasov--Maxwell--Boltzmann (VMB) systems for both two species and one species are studied in this paper. The analysis shows the effect of the Lorentz force induced by the electromagnetic field leads to some different structure of spectrum from the classical Boltzmann equation and the closely related VPB system. And the significant difference between the two-species VMB model and one-species VMB model are given. The structure in high frequency illustrates the hyperbolic structure of the Maxwell equation. Furthermore, the long time behaviors and the optimal convergence rates to the equilibrium of the VMB systems for both two species and one species are established based on the spectrum analysis, and in particular the phenomena of the electric field dominating and magnetic field dominating are observed for the one-species VMB system.

Research Area(s)

  • Vlasov–Maxwell–Boltzmann system, Lorentz force, spectrum structure, optimal convergence rates

Citation Format(s)

Spectrum structure and behaviors of the Vlasov-Maxwell-Boltzmann systems. / LI, Hai-Liang; YANG, Tong; ZHONG, Mingying.
In: SIAM Journal on Mathematical Analysis, Vol. 48, No. 1, 2016, p. 595-669.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review