Geodesic
Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions
Applications of Mathematics, Tome 56 (2011) no. 1, pp. 137-160.

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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(\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.
DOI : 10.1007/s10492-011-0013-4
Classification : 35A01, 35D30, 35Q30, 35Q35, 76N10
Keywords: steady compressible Navier-Stokes-Fourier system; weak solution; entropy inequality; Orlicz spaces; compensated compactness; renormalized solution 
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Novotný, Antonín; Pokorný, Milan. Weak solutions for steady compressible Navier-Stokes-Fourier system in two space dimensions. Applications of Mathematics, Tome 56 (2011) no. 1, pp. 137-160. doi : 10.1007/s10492-011-0013-4. http://geodesic.mathdoc.fr/articles/10.1007/s10492-011-0013-4/

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