On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

Shuichi Kawashima, Akitaka Matsumura, Takaaki Nishida

Research output: Contribution to journalArticle

70 Citations (Scopus)

Abstract

The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate t-5/4) as t→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.

Original languageEnglish
Pages (from-to)97-124
Number of pages28
JournalCommunications in Mathematical Physics
Volume70
Issue number2
DOIs
Publication statusPublished - 1979 Jun 1
Externally publishedYes

Fingerprint

Incompressible Navier-Stokes Equations
Boltzmann Equation
Navier-Stokes equation
Navier-Stokes Equations
Chapman-Enskog Expansion
Fluid
Compressible Navier-Stokes Equations
Asymptotically equivalent
fluids
Approximation
approximation
Decay Rate
Heat Equation
Nonlinear Equations
decay rates
heat
expansion

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation. / Kawashima, Shuichi; Matsumura, Akitaka; Nishida, Takaaki.

In: Communications in Mathematical Physics, Vol. 70, No. 2, 01.06.1979, p. 97-124.

Research output: Contribution to journalArticle

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