The regularity criterion for 3D Navier-Stokes Equations

TL;DR

This paper presents new criteria based on the gradient tensor for ensuring the regularity of solutions to the 3D Navier-Stokes equations, advancing previous theoretical results in fluid dynamics.

Contribution

It introduces improved regularity conditions focusing on a specific entry of the gradient tensor, refining earlier criteria by Cao, Titi, Zhou, and Pokorný.

Findings

Established new regularity criteria based on gradient tensor entries

Improved upon previous results by Cao, Titi, Zhou, and Pokorný

Contributed to the theoretical understanding of Navier-Stokes solutions

Abstract

In this article, we establish sufficient conditions for the regularity of solutions of Navier-Stokes equations based on one of the nine entries of the gradient tensor. We improve the recently results of C.S. Cao, E.S. Titi (Arch. Rational Mech.Anal. 202 (2011) 919-932) and Y. Zhou, M. Pokorn$\acute{y}$ (Nonlinearity 23, 1097-1107 (2010)).