Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

TL;DR

This paper introduces an improved Lady{z}enskaja-Prodi-Serrin regularity criterion for 3D Navier-Stokes solutions, utilizing weak space norms and a logarithmic time factor to enhance existing conditions.

Contribution

It presents a novel regularity criterion that combines weak L^p space norms with a logarithmic time improvement for the Navier-Stokes equations.

Findings

Establishes a new regularity criterion involving weak L^p norms.

Incorporates a logarithmic improvement in the time variable.

Provides conditions under which solutions remain regular.

Abstract

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time variable.