We consider a Navier-Stokes model for compressible fluids in one space dimension. We show that it can be approximated by a time-discrete scheme combining the discretization of a trivial stochastic differential equation and the application of a suitable monotonic rearrangement operator In addition, our result can be easily extended to a related Navier-Stokes-Poisson system.
@article{arxiv.1211.1764,
title = {Approximation of a simple Navier-Stokes model by monotonic rearrangement},
author = {Yann Brenier},
journal= {arXiv preprint arXiv:1211.1764},
year = {2012}
}