# Steady Navier- Stokes-Fourier system with slip boundary conditions

Abstract : We consider a problem modeling the steady flow of a compressible heat conducting Newtonian fluid subject to the slip boundary condition for the velocity. Assuming the pressure law of the form $p(\vr,\vt) \sim \vr^\gamma + \vr \vt$, we show (under additional assumptions on the heat conductivity and the viscosity) that for any $\gamma >1$ there exists a variational entropy solution to our problem (i.e. the weak formulation of the total energy balance is replaced by the entropy inequality and the global total energy balance). Moreover, if $\gamma > \frac 54$ (together with further restrictions on the heat conductivity), the solution is in fact a weak one. The results are obtained without any restriction on the size of the data.
Type de document :
Article dans une revue
Math. Models Methods Appl. Sci., 2014, 24 (4), pp.751-782

https://hal-univ-tln.archives-ouvertes.fr/hal-00998363
Contributeur : Antonin Novotny <>
Soumis le : dimanche 1 juin 2014 - 21:40:56
Dernière modification le : lundi 21 mars 2016 - 11:33:17

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• HAL Id : hal-00998363, version 1

### Citation

Didier Jesslé, Antonin Novotny, Milan Pokorny. Steady Navier- Stokes-Fourier system with slip boundary conditions. Math. Models Methods Appl. Sci., 2014, 24 (4), pp.751-782. 〈hal-00998363〉

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