# A note on the Prodi-Serrin conditions for the regularity of a weak solution to the Navier-Stokes equations

## TL;DR

This paper investigates relaxed Prodi-Serrin conditions for weak solutions of the Navier-Stokes equations, showing regularity without requiring initial data compatibility conditions.

## Contribution

It introduces a relaxed Prodi-Serrin criterion that ensures regularity of weak solutions without initial data compatibility constraints.

## Key findings

- Regularity achieved under relaxed conditions
- No compatibility condition needed for initial data
- Extends classical criteria for Navier-Stokes regularity

## Abstract

The paper is concerned with the regularity of weak solutions to the Navier-Stokes equations. The aim is to investigate on a relaxed Prodi-Serrin condition in order to obtain regularity for t > 0. The most interesting aspect of the result is that no compatibility condition is required to the initial data $v_0\in J^2(\OO) J2({\Omega})$.