On the interior regularity criteria of the 3-D Navier-Stokes equations involving two velocity components

TL;DR

This paper establishes interior regularity criteria for the 3-D Navier-Stokes equations based on two velocity components, showing that singularities require at least two components to blow up simultaneously.

Contribution

It introduces new criteria involving two velocity components that improve understanding of singularity formation in 3-D Navier-Stokes solutions.

Findings

Singular points necessitate at least two velocity components to blow up.

Provides conditions under which solutions remain regular.

Highlights the importance of component interactions in singularity development.

Abstract

We present some interior regularity criteria of the 3-D Navier-Stokes equations involving two components of the velocity. These results in particular imply that if the solution is singular at one point, then at least two components of the velocity have to blow up at the same point.