Stochastic Navier-Stokes-Fourier equations
Analysis of PDEs
2017-10-31 v1
Abstract
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. Stochastic effects are implemented through (i) random initial data, (ii) a forcing term in the momentum equation represented by a multiplicative white noise, (iii) random heat source in the internal energy balance. We establish existence of a weak martingale solution under physically grounded structural assumptions. As a byproduct of our theory we can show that stationary martingale solutions only exist in certain trivial cases.
Cite
@article{arxiv.1710.10497,
title = {Stochastic Navier-Stokes-Fourier equations},
author = {Dominic Breit and Eduard Feireisl},
journal= {arXiv preprint arXiv:1710.10497},
year = {2017}
}