Solvability of a steady boundary-value problem for the equations of one-temperature viscous compressible heat-conducting bifluids

TL;DR

This paper proves the existence of weak solutions for a boundary-value problem modeling steady flow of a two-component viscous, heat-conducting compressible fluid mixture, generalizing the Navier-Stokes-Fourier equations.

Contribution

It establishes the solvability of a complex two-fluid model without simplifying assumptions, extending the mathematical understanding of such systems.

Findings

Existence of weak solutions proven

No simplifying assumptions except temperature coincidence

Generalization of Navier-Stokes-Fourier model

Abstract

We consider a boundary-value problem describing the steady 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.