TY - JOUR

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

AU - Březina, Jan

AU - Kreml, Ondřej

AU - Mácha, Václav

N1 - Funding Information:
O.K. acknowledges the support of the GACˇR (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.
Publisher Copyright:
© 2016, Springer International Publishing.

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.

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U2 - 10.1007/s00021-016-0301-6

DO - 10.1007/s00021-016-0301-6

M3 - Article

AN - SCOPUS:85032175956

SN - 1422-6928

VL - 19

SP - 659

EP - 683

JO - Journal of Mathematical Fluid Mechanics

JF - Journal of Mathematical Fluid Mechanics

IS - 4

ER -