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Journal Articles Mathematical Models and Methods in Applied Sciences Year : 2014

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

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Didier Jesslé
• Function : Author
Antonin Novotny
Milan Pokorny
• Function : Author

#### 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.

#### Domains

Mathematics [math] Analysis of PDEs [math.AP]

### Dates and versions

hal-00998363 , version 1 (01-06-2014)

### Identifiers

• HAL Id : hal-00998363 , version 1

### Cite

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

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