2016/08/08 by Jan Březina, Ondřej Kreml, Václav Mácha
Mathematics · #math.AP
paper · pdf · doi:10.1007/s00021-016-0301-6
arXiv admin note: text overlap with arXiv:1111.4256 by other authors
arxiv created 2016/08/08 · arxiv updated 2016/11/23
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.