Dimension Reduction for the Full Navier-Stokes-Fourier system

作者:Brezina Jan*; Kreml Ondrej; Macha Vaclav
来源:Journal of Mathematical Fluid Mechanics, 2017, 19(4): 659-683.
DOI:10.1007/s00021-016-0301-6

摘要

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.

  • 出版日期2017-12