Global regular solutions for the Navier-stokes system with small initial data in $\Phi(2)$: an elementary approach

TL;DR

This paper proves the existence and regularity of solutions to the Navier-Stokes equations with small initial data in the space (2), using an elementary approach and relating to classical results.

Contribution

It introduces an elementary method to establish regular solutions for Navier-Stokes with small data in (2), connecting to classical theories.

Findings

Existence of regular solutions for small initial data in (2)

Regularity results for Navier-Stokes with small data

Relation to classical Navier-Stokes results

Abstract

We show existence and regularity result for the Navier Stokes system for small data in the space $\Phi(2)$, and we show relations with some classical results.