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Journal of Mathematical Fluid Mechanics

, Volume 19, Issue 4, pp 659–683 | Cite as

Dimension Reduction for the Full Navier–Stokes–Fourier system

  • Jan Březina
  • Ondřej Kreml
  • Václav MáchaEmail author
Article

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.

Keywords

Navier–Stokes–Fourier system dimension reduction relative entropy 

Mathematics Subject Classification

35Q35 76N15 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Institute of Mathematics of the Czech Academy of SciencesPraha 1Czech Republic
  3. 3.Industry-University Research CenterYonsei UniversitySeoulRepublic of Korea

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