An addendum to the paper: "Some elementary estimates for the Navier-Stokes system"

TL;DR

This paper proves the existence of global regular solutions for the Fourier transformed Navier-Stokes system with small initial data, complementing previous elementary estimates and using an iterative proof approach.

Contribution

It provides a proof of global regularity for the Fourier transformed Navier-Stokes system with small initial data, extending prior elementary estimates.

Findings

Existence of global regular solutions established

Small initial data condition required

Iterative proof method used

Abstract

In this paper we give a proof of the existence of global regular solutions to the Fourier transformed Navier-Stokes system with small initial data in $\Phi(2)$ via an iteration argument. The proof of the regularity theorem is a minor modification of the proof given in the paper "Some elementary estimates for the Navier-Stokes system". So this paper is intended to be just a complement to the afore mentioned paper.