Fast flow asymptotics for stochastic incompressible viscous fluids in $\mathbb{R}^2$ and SPDEs on graphs

TL;DR

This paper investigates the behavior of stochastic incompressible viscous fluids in two dimensions under fast flow conditions, using SPDEs on graphs to model the stream function and analyze asymptotic limits.

Contribution

It introduces a novel approach to describe fast flow asymptotics for stochastic fluids via SPDEs on graphs linked to the stream function.

Findings

Derivation of asymptotic behavior for stochastic fluid equations

Development of SPDE models on graphs for stream functions

Insights into the impact of fast advection on stochastic fluid dynamics

Abstract

Fast advection asymptotics for a stochastic reaction-diffusion-advection equation are studied in this paper. To describe the asymptotics, one should consider a suitable class of SPDEs defined on a graph, corresponding to the stream function of the underlying incompressible flow.