A regularity criterion in multiplier spaces to Navier-Stokes equations via the gradient of one velocity component

TL;DR

This paper establishes a new regularity criterion for weak solutions to the 3D Navier-Stokes equations, based on the gradient of a single velocity component within multiplier spaces, advancing understanding of solution regularity conditions.

Contribution

It introduces a novel regularity criterion involving the gradient of one velocity component in multiplier spaces, providing new insights into Navier-Stokes solution regularity.

Findings

Regularity criterion established via the gradient of one velocity component.

The criterion is formulated in the context of multiplier spaces.

Results contribute to understanding conditions for solution regularity.

Abstract

In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in multiplier spaces.