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

Shuichi Kawashima, Akitaka Matsumura, Takaaki Nishida

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74 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1979 Jun 1
Externally publishedYes


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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