Geodesic
Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 541-583.

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We consider the initial boundary value problem which describes unsteady polytropic motions of a multicomponent mixture of viscous compressible fluids in a bounded three-dimensional domain. The material derivative operator is supposed to be common for all components and defined by the average velocity of the mixture, however separate velocities of the components are preserved in other terms. The pressure is supposed to be common and depending on the total density via the polytropic equation of state. Except the above mentioned, we do not make any simplifications (including the structure of the viscosity matrix), i. e. all summands are preserved in the equations which are a natural generalization of the Navier–Stokes model which describes motions of one-component media. We proved the existence of weak solutions to the initial boundary value problem.
Keywords: existence theorem, unsteady boundary value problem, homogeneous mixture with multiple velocities, polytropic equation of state
Mots-clés : viscous compressible fluid, effective viscous flux. 
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A. E. Mamontov; D. A. Prokudin. Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 541-583. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a76/

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