Several almost critical regularity conditions based on one component of the solutions for 3D N-S Equations

TL;DR

This paper establishes new regularity conditions for weak solutions of the 3D Navier-Stokes equations, based on a single component of the solution, advancing understanding of solution regularity criteria.

Contribution

It introduces several almost critical regularity conditions involving one component of the solution, providing novel criteria for solution regularity in 3D Navier-Stokes equations.

Findings

Weak solutions become regular under new conditions involving u_3 or ∂_3u_3

Conditions are nearly critical, broadening previous regularity criteria

Results contribute to the understanding of solution behavior in fluid dynamics

Abstract

In this article, we establish several almost critical regularity conditions such that the weak solutions of the 3D Navier-Stokes equations become regular, based on one component of the solutions, say $u_3$ and $\partial_3u_3$.