Some Interior Regularity Criteria Involving Two Components for Weak Solutions to the 3D Navier–Stokes Equations

In this paper, we prove new local criteria in terms of the horizontal gradient of the horizontal velocity ∇huh\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \nabla _{h}u_{h}$$\end{document} for suitable weak solutions of the 3D Navier–Stokes equations. In addition, we present an alternative proof of some known interior criteria involving two components of suitable weak solutions to this system.