# 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.

https://hal-univ-tln.archives-ouvertes.fr/hal-00998363
Contributor : Antonin Novotny <>
Submitted on : Sunday, June 1, 2014 - 9:40:56 PM
Last modification on : Tuesday, July 3, 2018 - 1:02:18 PM

### Identifiers

• HAL Id : hal-00998363, version 1

### Citation

Didier Jesslé, Antonin Novotny, Milan Pokorny. Steady Navier- Stokes-Fourier system with slip boundary conditions. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2014, 24 (4), pp.751-782. ⟨hal-00998363⟩

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