Log improvement of the Prodi-Serrin criteria for Navier-Stokes equations

TL;DR

This paper enhances the Prodi-Serrin criterion for Navier-Stokes equations by establishing global regularity under a logarithmically improved integrability condition on the velocity field.

Contribution

It introduces a novel logarithmic refinement of the Prodi-Serrin criterion, broadening the class of solutions known to be globally regular.

Findings

Global regularity holds if |u|^5 / log(1+|u|) is integrable in space-time.

The result extends classical criteria by incorporating a logarithmic factor.

Provides a new condition for the regularity of Navier-Stokes solutions.

Abstract

This article is devoted to a Log improvement of Prodi-Serrin criterion for global regularity to solutions to Navier-Stokes equations in dimension 3. It is shown that the global regualrity holds under the condition that |u|^5/ log (1+|u|) is integrable in space time variables.