Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions

Antonín Novotný; Milan Pokorný

Applications of Mathematics (2011)

  • Volume: 56, Issue: 1, page 137-160
  • ISSN: 0862-7940

Abstract

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We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law p ( ϱ , ϑ ) ∼ ϱ γ + ϱ ϑ if γ > 1 and p ( ϱ , ϑ ) ∼ ϱ ln α ( 1 + ϱ ) + ϱ ϑ if γ = 1 , α > 0 , depending on the model for the heat flux.

How to cite

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Novotný, Antonín, and Pokorný, Milan. "Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions." Applications of Mathematics 56.1 (2011): 137-160. <http://eudml.org/doc/116508>.

@article{Novotný2011,
abstract = {We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law $p(\varrho ,\vartheta ) \sim \varrho ^\gamma + \varrho \vartheta $ if $\gamma >1$ and $p(\varrho ,\vartheta ) \sim \varrho \ln ^\alpha (1+\varrho ) + \varrho \vartheta $ if $\gamma =1$, $\alpha >0$, depending on the model for the heat flux.},
author = {Novotný, Antonín, Pokorný, Milan},
journal = {Applications of Mathematics},
keywords = {steady compressible Navier-Stokes-Fourier system; weak solution; entropy inequality; Orlicz spaces; compensated compactness; renormalized solution; steady compressible Navier-Stokes-Fourier system; weak solution; entropy inequality; Orlicz space; compensated compactness; renormalized solution},
language = {eng},
number = {1},
pages = {137-160},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions},
url = {http://eudml.org/doc/116508},
volume = {56},
year = {2011},
}

TY - JOUR
AU - Novotný, Antonín
AU - Pokorný, Milan
TI - Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions
JO - Applications of Mathematics
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 1
SP - 137
EP - 160
AB - We consider steady compressible Navier-Stokes-Fourier system in a bounded two-dimensional domain. We show the existence of a weak solution for arbitrarily large data for the pressure law $p(\varrho ,\vartheta ) \sim \varrho ^\gamma + \varrho \vartheta $ if $\gamma >1$ and $p(\varrho ,\vartheta ) \sim \varrho \ln ^\alpha (1+\varrho ) + \varrho \vartheta $ if $\gamma =1$, $\alpha >0$, depending on the model for the heat flux.
LA - eng
KW - steady compressible Navier-Stokes-Fourier system; weak solution; entropy inequality; Orlicz spaces; compensated compactness; renormalized solution; steady compressible Navier-Stokes-Fourier system; weak solution; entropy inequality; Orlicz space; compensated compactness; renormalized solution
UR - http://eudml.org/doc/116508
ER -

References

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