Localized non blow-up criterion of the Beale-Kato-Majda type for the 3D Euler equations

TL;DR

This paper establishes a localized criterion similar to Beale-Kato-Majda that prevents blow-up in solutions to the 3D incompressible Euler equations, enhancing understanding of solution regularity.

Contribution

It introduces a localized non blow-up criterion for the 3D Euler equations, extending classical Beale-Kato-Majda conditions to a more localized setting.

Findings

Proves a localized non blow-up theorem for 3D Euler equations

Extends classical blow-up criteria to localized conditions

Provides new insights into solution regularity and singularity prevention

Abstract

We prove a localized non blow-up theorem of the Beale-Kato-Majda type for the solution of the 3D incompressible Euler equations.