The Boltzmann equation and thirteen moments

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments.

Original languageEnglish
Pages (from-to)301-320
Number of pages20
JournalJapan Journal of Applied Mathematics
Volume7
Issue number2
DOIs
Publication statusPublished - 1990 Jun 1
Externally publishedYes

Fingerprint

Boltzmann equation
Decay Estimates
Boltzmann Equation
Moment
Initial value problems
Ordinary differential equations
Fourier transforms
Spectral Theory
Energy Method
Ludwig Boltzmann
Global Solution
Initial Value Problem
Fourier transform
Nonlinear Equations
Ordinary differential equation
Operator

Keywords

  • Boltzmann equation
  • energy method
  • Ljapunov function
  • stability of Maxwellian
  • thirteen moments

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Cite this

The Boltzmann equation and thirteen moments. / Kawashima, Shuichi.

In: Japan Journal of Applied Mathematics, Vol. 7, No. 2, 01.06.1990, p. 301-320.

Research output: Contribution to journalArticle

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