Weak solutions to the Navier-Stokes equations

TL;DR

This paper establishes an equivalence between Leray-Hopf weak solutions of the Navier-Stokes equations and a specific integral equation, enabling new insights into their properties.

Contribution

It introduces a new characterization of weak solutions via an integral equation, enhancing understanding of their structure and properties.

Findings

Proves equivalence between weak solutions and an integral equation

Derives properties of weak solutions using the integral formulation

Provides a new framework for analyzing Navier-Stokes weak solutions

Abstract

We prove the equivalence of being a Leray-Hopf weak solution to the Navier-Stokes equations in $\mathbb{R}^m, m \ge 3$, to satisfying a well known integral equation. We use this equation to derive some properties of these weak solutions.