### Abstract

Solutions of the nonlinear Boltzmann equation are constructed up to the first appearance of shocks in the corresponding fluid dynamics. This construction assumes the knowledge of solutions of the Euler equations for compressible gas flow. The Boltzmann solution is found as a truncated Hilbert expansion with a remainder, and the remainder term solves a weakly nonlinear equation which is solved by iteration. The solutions found have special initial values. They should serve as “outer expansions” to which initial layers, boundary layers and shock layers can be matched.

Original language | English (US) |
---|---|

Pages (from-to) | 651-666 |

Number of pages | 16 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 33 |

Issue number | 5 |

DOIs | |

State | Published - 1980 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*33*(5), 651-666. https://doi.org/10.1002/cpa.3160330506

**The fluid dynamic limit of the nonlinear boltzmann equation.** / Caflisch, Russel.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 33, no. 5, pp. 651-666. https://doi.org/10.1002/cpa.3160330506

}

TY - JOUR

T1 - The fluid dynamic limit of the nonlinear boltzmann equation

AU - Caflisch, Russel

PY - 1980

Y1 - 1980

N2 - Solutions of the nonlinear Boltzmann equation are constructed up to the first appearance of shocks in the corresponding fluid dynamics. This construction assumes the knowledge of solutions of the Euler equations for compressible gas flow. The Boltzmann solution is found as a truncated Hilbert expansion with a remainder, and the remainder term solves a weakly nonlinear equation which is solved by iteration. The solutions found have special initial values. They should serve as “outer expansions” to which initial layers, boundary layers and shock layers can be matched.

AB - Solutions of the nonlinear Boltzmann equation are constructed up to the first appearance of shocks in the corresponding fluid dynamics. This construction assumes the knowledge of solutions of the Euler equations for compressible gas flow. The Boltzmann solution is found as a truncated Hilbert expansion with a remainder, and the remainder term solves a weakly nonlinear equation which is solved by iteration. The solutions found have special initial values. They should serve as “outer expansions” to which initial layers, boundary layers and shock layers can be matched.

UR - http://www.scopus.com/inward/record.url?scp=84980175331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980175331&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160330506

DO - 10.1002/cpa.3160330506

M3 - Article

AN - SCOPUS:84980175331

VL - 33

SP - 651

EP - 666

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 5

ER -