We consider the Navier--Stokes--Fourier system in a bounded domain Ω⊂Rd, 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.
@article{arxiv.2009.08207,
title = {Navier-Stokes-Fourier system with general boundary conditions},
author = {Eduard Feireisl and Antonin Novotny},
journal= {arXiv preprint arXiv:2009.08207},
year = {2021}
}