English

Dimension reduction for the full Navier-Stokes-Fourier system

Analysis of PDEs 2016-11-23 v1

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

Cite

@article{arxiv.1608.02343,
  title  = {Dimension reduction for the full Navier-Stokes-Fourier system},
  author = {Jan Březina and Ondřej Kreml and Václav Mácha},
  journal= {arXiv preprint arXiv:1608.02343},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1111.4256 by other authors