Derivation of ohm's law from the kinetic equations

Juhi Jang, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

The goal of this article is to give a formal derivation of Ohm's law of magnetohydrodynamics (MHD) starting from the Vlasov-Maxwell-Boltzmann system. The derivation is based on various physical scalings and the moment methods when the Knudsen number goes to zero. We also give a derivation of the so-called Hall effect as well as other limit models such as the Navier-Stokes- Maxwell system. Our results include both the compressible and incompressible MHD models.

Original languageEnglish (US)
Pages (from-to)3649-3669
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number5
DOIs
StatePublished - 2012

Fingerprint

Magnetohydrodynamics
Kinetic Equation
Hall Effect
Maxwell System
Knudsen number
Kinetics
Moment Method
Navier-Stokes System
Hall effect
Method of moments
Ludwig Boltzmann
Scaling
Zero
Model

Keywords

  • Hall effect
  • Hydrodynamic limit
  • Magnetohydrodynamics
  • Ohm's law
  • Vlasov-Maxwell-Boltzmann system

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Derivation of ohm's law from the kinetic equations. / Jang, Juhi; Masmoudi, Nader.

In: SIAM Journal on Mathematical Analysis, Vol. 44, No. 5, 2012, p. 3649-3669.

Research output: Contribution to journalArticle

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