Global Wellposedness for a Certain Class of Large Initial Data for the 3D Navier–Stokes Equations

In this article, we consider a special class of initial data to the 3D Navier–Stokes equations on the torus, in which there is a certain degree of orthogonality in the components of the initial data. We showed that, under such conditions, the Navier–Stokes equations are globally wellposed. We also showed that there exists large initial data, in the sense of the critical norm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B^{-1}_{\infty,\infty}}$$\end{document} that satisfies the conditions that we considered.