Regularity of weak solutions to the Navier-Stokes equations (III)-frequency overlapping

TL;DR

This paper investigates the regularity of weak solutions to the Navier-Stokes equations, focusing on frequency overlapping techniques to establish conditions under which solutions are smooth.

Contribution

It introduces a novel frequency overlapping approach to prove regularity of Leray-Hopf solutions with initial data in L^2(R^3).

Findings

Leray-Hopf solutions with initial data in L^2(R^3) are regular.

Frequency overlapping methods can be used to analyze solution regularity.

The paper extends previous regularity results using new analytical techniques.

Abstract

If $u$ is a Leray-Hopf solution to the Navier-Stokes equations with the initial data in $ L^2(\mathbb{R}^3)$, then $u$ is regular.