The Boltzmann equation and thirteen moments

Research output: Contribution to journalArticlepeer-review

47 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

Keywords

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

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'The Boltzmann equation and thirteen moments'. Together they form a unique fingerprint.

Cite this