Strong solutions to the Navier-Stokes-Fourier system with slip-inflow boundary conditions

TL;DR

This paper proves the existence of strong solutions for a steady compressible heat-conducting fluid flow in a 3D channel with slip-inflow boundary conditions, under near-constant flow data and high energy dissipation.

Contribution

It establishes the existence of strong solutions to the Navier-Stokes-Fourier system with slip-inflow boundary conditions for near-constant data and large dissipation.

Findings

Existence of strong solutions under specified conditions.

Solutions are valid for flows close to a constant state.

High dissipation is crucial for the existence proof.

Abstract

We consider a system of partial differential equations describing the steady flow of a compressible heat conducting Newtonian fluid in a three-dimensional channel with inflow and outflow part. We show the existence of a strong solution provided the data are close to a constant, but nontrivial flow with sufficiently large dissipation in the energy equation.