Abstract: 
We consider the following system of equations
\begin{equation}
\begin{array}{c}
{\rm div}\, (\varrho \mathbf{u}) = 0,\
{\rm div}\, (\varrho \mathbf{u} \otimes \mathbf{u})  {\rm div} {\mathbf{S}}+ \nabla {\pi} =\varrho\mathbf{f},\
{\rm div}\, (\varrho E \mathbf{u}) + {\rm div}\, (\mathbf {Q}+\pi\mathbf{u} \mathbf{S}\mathbf{u})= \varrho\mathbf{f}\cdot \mathbf{u},\
{\rm div}\, (\varrho Y_k \mathbf{u})+ {\rm div}\, \mathbf {F}_k = m_k\omega_{k},\quad k=1,\dots, L
\end{array}
\end{equation}
which describes the steady flow of a compressible heat conducting mixture of gases whose component may chemically react, where only the barycentric velocity is taken into account. We consider either the noslip or the Navier boundary conditions for the velocity and the Newton boundary condition for the temperature. Based on papers [1][3] we present existence results of weak and variational entropy solutions in different situations.
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{\bf References}
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[1] Giovangigli, V., Pokorn\`y, M., Zatorska, E.: \emph{On the steady flow of reactive gaseous mixture},
Analysis (Berlin) 35, no. 4, 319341 (2015).
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[2] Piasecki, T., Pokorn\`y, M.: \emph{Weak and variational entropy solutions to the system describing steady flow
of a compressible reactive mixture}, Nonlinear Anal. (TMA) 159 (2017), 365392 (2017).
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[3] Piasecki, T., Pokorn\`y, M.: \emph{On steady solutions to a model of chemically reacting heat conducting compressible mixture with slip boundary conditions}, to appear in Contemporary Mathematics (2018). 
