Some remarks on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem

TL;DR

This paper explores local regularity properties of suitable weak solutions to the Navier-Stokes equations, building on foundational work by Caffarelli-Kohn-Nirenberg to deepen understanding of solution regularity conditions.

Contribution

It provides new insights into the partial regularity of weak solutions to the Navier-Stokes Cauchy problem, extending previous theoretical frameworks.

Findings

Enhanced understanding of local regularity conditions.

Refined criteria for partial regularity of weak solutions.

Connections to classical results by Caffarelli-Kohn-Nirenberg.

Abstract

The aim of the paper is to investigate on some questions of local regularity of a suitable weak solution to the Navier-Stokes Cauchy problem. The results are obtained in the wake of the ones, well known, by Caffarelli-Kohn-Nirenberg.