### Abstract

Shock waves in gas dynamics can be described by the Euler Navier-Stokes, or Boltzmann equations. We prove the existence of shock profile solutions of the Boltzmann equation for shocks which are weak. The shock is written as a truncated expansion in powers of the shock strength, the first two terms of which come exactly from the Taylor tanh (x) profile for the Navier-Stokes solution. The full solution is found by a projection method like the Lyapunov-Schmidt method as a bifurcation from the constant state in which the bifurcation parameter is the difference between the speed of sound c_{0} and the shock speed s.

Original language | English (US) |
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Pages (from-to) | 161-194 |

Number of pages | 34 |

Journal | Communications In Mathematical Physics |

Volume | 86 |

Issue number | 2 |

DOIs | |

State | Published - Jun 1982 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Caflisch, R. E., & Nicolaenko, B. (1982). Shock profile solutions of the Boltzmann equation.

*Communications In Mathematical Physics*,*86*(2), 161-194. https://doi.org/10.1007/BF01206009