Compressible fluid flows driven by stochastic forcing

TL;DR

This paper studies the behavior of compressible fluid flows under stochastic forces using a semi-deterministic approach, extending methods from incompressible models to the compressible Navier-Stokes system.

Contribution

It introduces a novel semi-deterministic framework for analyzing stochastic compressible flows, including a broad class of stochastic forces like white noise and random kicks.

Findings

Established measurability of solutions under stochastic forcing.

Extended stochastic analysis techniques from incompressible to compressible fluids.

Provided a foundation for future probabilistic studies of compressible fluid dynamics.

Abstract

We consider the Navier-Stokes system describing the motion of a compressible barotropic fluid driven by stochastic external forces. Our approach is semi-deterministic, based on solving the system for each fixed representative of the random variable and applying an abstract result on measurability of multi-valued maps. The class of admissible driving forces includes the (temporal) white noise and the random kicks, considered recently in the context of incompressible fluid models.