We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary conditions for the temperature and hence energetically open. We show that, in contrast with the energetically closed system, there exists a stationary solution. Our approach is based on new global-in-time estimates which rely on the non-homogeneous boundary conditions combined with estimates for the pressure.
@article{arxiv.2102.04178,
title = {Stationary solutions in thermodynamics of stochastically forced fluids},
author = {Dominic Breit and Eduard Feireisl and Martina Hofmanová},
journal= {arXiv preprint arXiv:2102.04178},
year = {2021}
}