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arXiv · 1608.02343

Dimension reduction for the full Navier-Stokes-Fourier system

Jan Březina·Ondřej Kreml·Václav Mácha
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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.

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Jan Březina, Ondřej Kreml, Václav Mácha. 2016-08-08. Dimension reduction for the full Navier-Stokes-Fourier system. https://doi.org/10.1007/s00021-016-0301-6

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