Steady 3D viscous compressible flows with adiabatic exponent $\gamma\in (1,\infty)$

TL;DR

This paper proves the existence of weak solutions for steady 3D viscous compressible flows governed by Navier-Stokes equations with adiabatic exponent greater than one, covering various gas types.

Contribution

It establishes the existence of weak solutions for stationary 3D compressible Navier-Stokes equations with a broad range of adiabatic exponents, extending previous results.

Findings

Existence of weak solutions for $ abla eq 1$

Applicable to monoatomic, diatomic, and polyatomic gases

Valid for bounded domains with no-slip boundary conditions

Abstract

The Navier-Stokes equations for compressible barotropic flow in the stationary three dimensional case are considered. It is assumed that a fluid occupies a bounded domain and satisfies the no-slip boundary condition. The existence of a weak solution under the assumption that the adiabatic exponent satisfies $\gamma>1$ is proved. These results cover the cases of monoatomic, diatomic, and polyatomic gases.