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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 541–583
DOI: https://doi.org/10.17377/semi.2016.13.044
(Mi semr694)
 

This article is cited in 12 scientific papers (total in 12 papers)

Differentical equations, dynamical systems and optimal control

Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids

A. E. Mamontov, D. A. Prokudin

Lavrentyev Institute of Hydrodynamics, pr. Lavrent'eva, 15, 630090, Novosibirsk, Russia
References:
Abstract: 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, viscous compressible fluid, homogeneous mixture with multiple velocities, polytropic equation of state, effective viscous flux.
Funding agency Grant number
Russian Science Foundation 15-11-20019
Received February 26, 2016, published June 26, 2016
Document Type: Article
UDC: 517.95
MSC: 35A05
Language: Russian
Citation: A. E. Mamontov, D. A. Prokudin, “Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids”, Sib. Èlektron. Mat. Izv., 13 (2016), 541–583
Citation in format AMSBIB
\Bibitem{MamPro16}
\by A.~E.~Mamontov, D.~A.~Prokudin
\paper Solubility of initial boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 541--583
\mathnet{http://mi.mathnet.ru/semr694}
\crossref{https://doi.org/10.17377/semi.2016.13.044}
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