Regularity Criteria For Strong Solutions To The 3D Navier-Stokes Equations

TL;DR

This paper establishes new regularity criteria ensuring global existence of strong solutions to the 3D Navier-Stokes equations, improving previous results especially when forces are negligible.

Contribution

It introduces novel regularity criteria that guarantee global solutions and extends the known time intervals of regularity for the Navier-Stokes equations.

Findings

Proved global existence of strong solutions under new criteria.

Improved the regularity time interval for negligible forces.

Extended previous regularity results in the literature.

Abstract

In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known time interval of regularity obtained in [9].