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

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.