### Abstract

This chapter is a summary of the work concerning the Navier-Stokes equation derived from the discrete Boltzmann equation. It considers a model of gas whose molecular velocities are restricted to a set of m constant vectors v_{1},v_{m} in IR^{n}. The purpose of this chapter is to study the hydrodynamical equations derived from the discrete Boltzmann equation by applying the Chapman-Enskog method. This chapter shows that the Navier-Stokes equation is transformed into a symmetric system by change of the dependent variable. It is known that the Navier-Stokes equation can be transformed into a coupled system of a symmetric hyperbolic system and a symmetric strongly parabolic system, by changing the dependent variable from w t o u.

Original language | English |
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Pages (from-to) | 15-30 |

Number of pages | 16 |

Journal | North-Holland Mathematics Studies |

Volume | 160 |

Issue number | C |

DOIs | |

Publication status | Published - 1989 Jan 1 |

Externally published | Yes |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

*North-Holland Mathematics Studies*,

*160*(C), 15-30. https://doi.org/10.1016/S0304-0208(08)70504-8