Reynolds Averaged Solutions of the Navier-Stokes Equation

TL;DR

This paper discusses the mean of Young measure solutions for the Navier-Stokes equations, showing they are PDE solutions within the class considered by Leray and Hopf, under general initial conditions.

Contribution

It establishes that the mean of Young measure solutions for Navier-Stokes equations are PDE solutions in the Leray-Hopf class for general initial conditions.

Findings

Mean of Young measure solutions are PDE solutions.

Applicable to Navier-Stokes equations with general initial conditions.

Extends understanding of solution classes for Navier-Stokes.

Abstract

The mean of Young measure solutions for the Navier-Stokes equations with general initial conditions are PDE solutions of the Navier-Stokes equation of the class considered by Leray and Hopf.