Solutions of equations of viscous hydrodynamics via stochastic perturbations of inviscid flows

TL;DR

This paper presents a stochastic perturbation approach to solve viscous hydrodynamics equations, connecting inviscid flows with Burgers, Reynolds, and Navier-Stokes equations through diffeomorphism group perturbations.

Contribution

It introduces a novel stochastic perturbation method that transforms inviscid flow solutions into viscous hydrodynamics solutions within the diffeomorphism group framework.

Findings

Perturbed flows solve Burgers and Reynolds equations

Special external forces convert Reynolds to Navier-Stokes solutions

Method links inviscid and viscous flow equations via stochastic perturbations

Abstract

We introduce a special stochastic perturbation of the flow of diffuse matter as a curve in the group of diffeomorphisms of flat n-dimensional torus such that the perturbed system yields a solution of Burgers equation in the tangent space at unit of the diffeomorphism group. The same perturbation of the flow of perfect incompressible fluid yields a solution of Reynolds type equation but under some special external force on the diffeomorphism group it transforms into a solution of Navier-Stokes equation without external force.