On the steady compressible Navier-Stokes-Fourier system

TL;DR

This paper proves the existence of weak solutions for the steady compressible Navier-Stokes-Fourier system in a bounded domain, using a novel approximation method that ensures density bounds and simplifies the limit process.

Contribution

It introduces a new approximation approach that guarantees uniform density bounds, enabling the existence proof without complex technical limits.

Findings

Existence of weak solutions for large data

A new approximation method for density bounds

Simplified limit passage process

Abstract

We study the motion of the steady compressible heat conducting viscous fluid in a bounded three dimensional domain governed by the compressible Navier-Stokes-Fourier system. Our main result is the existence of a weak solution to these equations for arbitrarily large data. A key element of the proof is a special approximation of the original system guaranteeing pointwise uniform boundedness of the density. Therefore the passage to the limit omits tedious technical tricks required by the standard theory. Basic estimates on the solutions are possible to obtain by a suitable choice of physically reasonable boundary conditions.