Dimension reduction for the full Navier-Stokes-Fourier system

0480573 - MÚ 2018 RIV CH eng J - Článek v odborném periodiku
Březina, J. - Kreml, Ondřej - Mácha, Václav
Dimension reduction for the full Navier-Stokes-Fourier system.
Journal of Mathematical Fluid Mechanics. Roč. 19, č. 4 (2017), s. 659-683. ISSN 1422-6928. E-ISSN 1422-6952
Grant CEP: GA ČR GA13-00522S
Institucionální podpora: RVO:67985840
Klíčová slova: Navier–Stokes–Fourier system * dimension reduction * relative entropy
Obor OECD: Pure mathematics
Impakt faktor: 1.013, rok: 2017
https://link.springer.com/article/10.1007%2Fs00021-016-0301-6

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.
Trvalý link: http://hdl.handle.net/11104/0276321