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Solvability of a Problem for the Equations of the Dynamics of One-Temperature Mixtures of Heat-Conducting Viscous Compressible Fluids

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Abstract

A system of partial differential equations governing the three-dimensional unsteady flow of a homogeneous two-component mixture of heat-conducting viscous compressible fluids (gases) is considered within the multivelocity approach. The model is complete in the sense that it retains all terms in the equations, which are a natural generalization of the Navier–Stokes–Fourier model for the motion of a single-component medium. The existence of weak solutions to the initial–boundary value problem describing the flow in a bounded domain is proved globally in time and the input data.

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Authors and Affiliations

  1. Lavrentiev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. E. Mamontov & D. A. Prokudin

Authors
  1. A. E. Mamontov
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  2. D. A. Prokudin
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Correspondence to A. E. Mamontov.

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Translated by I. Ruzanova

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Mamontov, A.E., Prokudin, D.A. Solvability of a Problem for the Equations of the Dynamics of One-Temperature Mixtures of Heat-Conducting Viscous Compressible Fluids. Dokl. Math. 99, 273–276 (2019). https://doi.org/10.1134/S1064562419030074

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  • DOI: https://doi.org/10.1134/S1064562419030074

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