### 抄録

The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments.

元の言語 | English |
---|---|

ページ（範囲） | 301-320 |

ページ数 | 20 |

ジャーナル | Japan Journal of Applied Mathematics |

巻 | 7 |

発行部数 | 2 |

DOI | |

出版物ステータス | Published - 1990 6 1 |

外部発表 | Yes |

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### ASJC Scopus subject areas

- Engineering(all)
- Applied Mathematics

### これを引用

**The Boltzmann equation and thirteen moments.** / Kawashima, Shuichi.

研究成果: Article

*Japan Journal of Applied Mathematics*, 巻. 7, 番号 2, pp. 301-320. https://doi.org/10.1007/BF03167846

}

TY - JOUR

T1 - The Boltzmann equation and thirteen moments

AU - Kawashima, Shuichi

PY - 1990/6/1

Y1 - 1990/6/1

N2 - The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments.

AB - The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments.

KW - Boltzmann equation

KW - energy method

KW - Ljapunov function

KW - stability of Maxwellian

KW - thirteen moments

UR - http://www.scopus.com/inward/record.url?scp=0009326251&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009326251&partnerID=8YFLogxK

U2 - 10.1007/BF03167846

DO - 10.1007/BF03167846

M3 - Article

AN - SCOPUS:0009326251

VL - 7

SP - 301

EP - 320

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 2

ER -