Geodesic
Solubility of a~stationary boundary-value problem for the equations of motion of a~one-temperature mixture of viscous compressible heat-conducting fluids
Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 554-579

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We consider a boundary-value problem describing the stationary motion of a two-component mixture of viscous compressible heat-conducting fluids in a bounded domain. We make no simplifying assumptions except for postulating the coincidence of phase temperatures (which is physically justified in certain situations), that is, we retain all summands in equations that are a natural generalization of the Navier–Stokes–Fourier model of the motion of a one-component medium. We prove the existence of weak generalized solutions of the problem.
Keywords: existence theorem, stationary boundary-value problem, viscous compressible heat-conducting fluid, homogeneous two-speed mixture, effective viscous flow. 
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     author = {A. E. Mamontov and D. A. Prokudin},
     title = {Solubility of a~stationary boundary-value problem for the equations of motion of a~one-temperature mixture of viscous compressible heat-conducting fluids},
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A. E. Mamontov; D. A. Prokudin. Solubility of a~stationary boundary-value problem for the equations of motion of a~one-temperature mixture of viscous compressible heat-conducting fluids. Izvestiya. Mathematics , Tome 78 (2014) no. 3, pp. 554-579. http://geodesic.mathdoc.fr/item/IM2_2014_78_3_a6/