### 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 language | English |
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Pages (from-to) | 97-124 |

Number of pages | 28 |

Journal | Communications in Mathematical Physics |

Volume | 70 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 1 1979 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*70*(2), 97-124. https://doi.org/10.1007/BF01982349

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

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 70, no. 2, pp. 97-124. https://doi.org/10.1007/BF01982349

}

TY - JOUR

T1 - On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

AU - Kawashima, Shuichi

AU - Matsumura, Akitaka

AU - Nishida, Takaaki

PY - 1979/6/1

Y1 - 1979/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0040193736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040193736&partnerID=8YFLogxK

U2 - 10.1007/BF01982349

DO - 10.1007/BF01982349

M3 - Article

AN - SCOPUS:0040193736

VL - 70

SP - 97

EP - 124

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -