Stability of the nonrelativistic Vlasov-Maxwell-Boltzmann system for angular non-cutoff potentials

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)159-204
Journal / PublicationKinetic and Related Models
Volume6
Issue number1
Online publishedDec 2012
Publication statusPublished - Mar 2013

Abstract

Although there recently have been extensive studies on the pertur-bation theory of the angular non-cutoff Boltzmann equation (cf. [4] and [17]), it remains mathematically unknown when there is a self-consistent Lorentz force coupled with the Maxwell equations in the nonrelativistic approximation. In the paper, for perturbative initial data with suitable regularity and integrabil-ity, we establish the large time stability of solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann system with physical angular non-cutoff inter-molecular collisions including the inverse power law potentials, and also obtain as a byproduct the convergence rates of solutions. The proof is based on a new time-velocity weighted energy method with two key technical parts: one is to introduce the exponentially weighted estimates into the non-cutoff Boltzmann operator and the other to design a delicate temporal energy X(t)-norm to ob-tain its uniform bound. The result also extends the case of the hard sphere model considered by Guo [Invent. Math. 153(3): 593-630 (2003)] to the general collision potentials. © American Institute of Mathematical Sciences.

Research Area(s)

  • Energy method, Non-cutoff potentials, The Vlasov-Maxwell-Boltzmann system, Time-velocity weight