### 抄録

It is well known that the full Navier–Stokes–Fourier system does not possess a strong solution in three dimensions which causes problems in applications. However, when modeling the flow of a fluid in a thin long pipe, the influence of the cross section can be neglected and the flow is basically one-dimensional. This allows us to deal with strong solutions which are more convenient for numerical computations. The goal of this paper is to provide a rigorous justification of this approach. Namely, we prove that any suitable weak solution to the three-dimensional NSF system tends to a strong solution to the one-dimensional system as the thickness of the pipe tends to zero.

元の言語 | 英語 |
---|---|

ページ（範囲） | 659-683 |

ページ数 | 25 |

ジャーナル | Journal of Mathematical Fluid Mechanics |

巻 | 19 |

発行部数 | 4 |

DOI | |

出版物ステータス | 出版済み - 12 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics

### これを引用

*Journal of Mathematical Fluid Mechanics*,

*19*(4), 659-683. https://doi.org/10.1007/s00021-016-0301-6

**Dimension Reduction for the Full Navier–Stokes–Fourier system.** / Březina, Jan; Kreml, Ondřej; Mácha, Václav.

研究成果: ジャーナルへの寄稿 › 記事

*Journal of Mathematical Fluid Mechanics*, 巻. 19, 番号 4, pp. 659-683. https://doi.org/10.1007/s00021-016-0301-6

}

TY - JOUR

T1 - Dimension Reduction for the Full Navier–Stokes–Fourier system

AU - Březina, Jan

AU - Kreml, Ondřej

AU - Mácha, Václav

PY - 2017/12/1

Y1 - 2017/12/1

N2 - It is well known that the full Navier–Stokes–Fourier system does not possess a strong solution in three dimensions which causes problems in applications. However, when modeling the flow of a fluid in a thin long pipe, the influence of the cross section can be neglected and the flow is basically one-dimensional. This allows us to deal with strong solutions which are more convenient for numerical computations. The goal of this paper is to provide a rigorous justification of this approach. Namely, we prove that any suitable weak solution to the three-dimensional NSF system tends to a strong solution to the one-dimensional system as the thickness of the pipe tends to zero.

AB - It is well known that the full Navier–Stokes–Fourier system does not possess a strong solution in three dimensions which causes problems in applications. However, when modeling the flow of a fluid in a thin long pipe, the influence of the cross section can be neglected and the flow is basically one-dimensional. This allows us to deal with strong solutions which are more convenient for numerical computations. The goal of this paper is to provide a rigorous justification of this approach. Namely, we prove that any suitable weak solution to the three-dimensional NSF system tends to a strong solution to the one-dimensional system as the thickness of the pipe tends to zero.

UR - http://www.scopus.com/inward/record.url?scp=85032175956&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032175956&partnerID=8YFLogxK

U2 - 10.1007/s00021-016-0301-6

DO - 10.1007/s00021-016-0301-6

M3 - Article

AN - SCOPUS:85032175956

VL - 19

SP - 659

EP - 683

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

SN - 1422-6928

IS - 4

ER -