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Dimension Reduction for the Full Navier–Stokes–Fourier system

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Abstract

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.

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Authors and Affiliations

  1. Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo, 152-8550, Japan

    Jan Březina

  2. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Ondřej Kreml

  3. Industry-University Research Center, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul, 03722, Republic of Korea

    Václav Mácha

Authors
  1. Jan Březina
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  2. Ondřej Kreml
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  3. Václav Mácha
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Corresponding author

Correspondence to Václav Mácha.

Additional information

Communicated by G.P. Galdi

O.K. acknowledges the support of the GAČR (Czech Science Foundation) project GA13-00522S in the general framework of RVO: 67985840. The research of V.M. has been supported by the Grant NRF-20151009350.

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Březina, J., Kreml, O. & Mácha, V. Dimension Reduction for the Full Navier–Stokes–Fourier system. J. Math. Fluid Mech. 19, 659–683 (2017). https://doi.org/10.1007/s00021-016-0301-6

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  • DOI: https://doi.org/10.1007/s00021-016-0301-6

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