Navier-Stokes-Fourier system with general boundary conditions

TL;DR

This paper introduces a new framework for weak solutions to the Navier-Stokes-Fourier system with realistic boundary conditions, proving global existence and uniqueness principles.

Contribution

It develops a novel concept of weak solutions satisfying a relative energy inequality for the Navier-Stokes-Fourier system with general boundary conditions.

Findings

Existence of global weak solutions for finite energy initial data.

Weak solutions satisfy a relative energy inequality.

Weak-strong uniqueness principle holds for the solutions.

Abstract

We consider the Navier--Stokes--Fourier system in a bounded domain $\Omega \subset R^d$, $d=2,3$, with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative energy inequality. The weak solutions exist globally in time for any finite energy initial data and comply with the weak--strong uniqueness principle.