Dimension Reduction for the Full Navier–Stokes–Fourier system

Jan Březina, Ondřej Kreml, Václav Mácha

Research output: Contribution to journalArticle

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)659-683
Number of pages25
JournalJournal of Mathematical Fluid Mechanics
Volume19
Issue number4
DOIs
Publication statusPublished - Dec 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

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